Experts are tested by Chegg as specialists in their subject area We review their content and useCalculate the iterated integral 2 0 1 0 (x y)2 dx dy Expert Answer Who are the experts? If y = \(\sqrt{\frac{sec\,x1}{sec\,x1}}\) then dy/dx = ?
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(x+1)dy/dx-y=e^3x(x+1)^2-See the answer See the answer See the answer done loading Calculate the iterated integral 4 1 2 x y y x dy dx Expert Answer Who are the experts?Popular Problems Calculus Find dy/dx 2xyy^2=1 2xy − y2 = 1 2 x y y 2 = 1 Differentiate both sides of the equation d dx (2xy−y2) = d dx (1) d d x ( 2 x y y 2) = d d x ( 1) Differentiate the left side of the equation Tap for more steps By the Sum Rule, the derivative of 2 x y − y 2 2 x y y 2 with respect to x x is d d x 2
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Question Calculate the iterated integral 4 1 2 x y y x dy dx This problem has been solved! The solution of the differential equation `(1y^(2)) tan^(1) x dx y(1x^(2)) dy = 0` is asked in Differential Equations by PoojaBhatt ( 994k points) class12 The order and the degree of the differential equation ` y = x (dy)/(dx) 2/(dy//dx)` are A 1,2 B 1,3 C 2,1 D 1,1
Example 9 Find the general solution of the differential equation 𝑑𝑦/𝑑𝑥= (𝑥1)/ (2−𝑦) , (𝑦≠2) 𝑑𝑦/𝑑𝑥= (𝑥 1)/ (2 − 𝑦) , (𝑦≠2) (2 − y) dy = (x 1) dx Integrating both sides ∫1 〖 (2−𝑦)𝑑𝑦=〗 ∫1 (𝑥1)𝑑𝑥 2y − 𝑦^2/2 = 𝑥^2/2 x c 〖4𝑦 − 𝑦〗^2/2 = (𝑥KEAM 11 If y= sin 2 cot 1√(1x/1x), then (dy/dx) is equal to (A) 2 sin 2x (B) sin 2x (1/2) (D) (1/2) (E) cos 2x Check AnsWeekly Subscription $249 USD per week until cancelled Monthly Subscription $799 USD per month until cancelled Holidays Promotion Annual Subscription $1999 USD for 12 months (40% off)
Homework Equations The Attempt at a Solution//wwwquoracom/Whatisthesolutionoffracdydx1x2y2 \frac {dy} {dx}=1x^2y^2, Given Here, \frac {dy} {dx} represents the derivative of y with respect to x I will solve for x and y, treating y as a function of x (essentially y=f (x)) \int \frac {dy} {dx}dx=\int 1x^2y^2dx dxdyD y d x = y x Separating the variables, the given differential equation can be written as 1 y d y = 1 x d x – – – ( i) With the separating the variable technique we must keep the terms d y and d x in the numerators with their respective functions Now integrating both sides of the equation (i), we have ∫ 1 y d y = ∫ 1 x d x
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8 marks (b) Determine the values of, A B and C for 3 2 1 y Ax B x Cx = − , if 2 dy dx = 2 2 1 d y dx = at the point 2,1 7 marks 19/ 29 If 2 2 4 3 5 8 y x xy − − =, find dy dx in terms of x and y Hence evaluate dy dx when 0 dy 2 and x = 5 marks 30 (a) Given 2 (1) x y x = and (2 dy Ax x B dx x =Find the values of ASolve the initial value problems x^2 dy/dx = 4x^2 x 2/ (x 1) (y 1), y (1) = 1 x^2 dy/dx 3xy = x^4 ln (x) 1, y (1) = 0 Solve the Equation dy/dx y/x 2 = 5 (x 2)y^1/2 Determine whether the equation is exact if it is then solve it 2/Squareroot 1 x^2 y cos (xy) dx x cos (xy) y^1/3 dy = 0 Solve the Equation dy/dx = xCalculus Find dy/dx y=1/ (x^2) y = 1 x2 y = 1 x 2 Differentiate both sides of the equation d dx (y) = d dx ( 1 x2) d d x ( y) = d d x ( 1 x 2) The derivative of y y with respect to x x is y' y ′ y' y ′ Differentiate the right side of the equation Tap for more steps
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Let's simplify it First dy/dx = (y/x 1)/(y/x 1) Taking y = vx dy/dx = v xdv/dx Therefore, dx/x = (v 1)dv / (v^2 1) Integrating we get log (1/x) logc = arctan (y/x) 1/2 logTo ask Unlimited Maths doubts download Doubtnut from https//googl/9WZjCW `x(1y^2)dxy(1x^2) dy=0` 1 2y −1 ⋅ dy dx = 1 integrating ∫ 1 2y −1 dy dx dx = ∫ dx ∫ 1 2y −1 dy = ∫ dx 1 2 ln(2y − 1) = x C ln(2y −1) = 2x C 2y −1 = e2xC = Ce2x
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I'm stuck on solving the following differential equation $$(x^21)(y^21)dx(x1)(y2)dy=0$$ Obviously it's not exact, because $\frac{d((x^21)(y^21))}{dy}\neq\fracCalculus Find dy/dx y^2= (x1)/ (x1) y2 = x − 1 x 1 y 2 = x 1 x 1 Differentiate both sides of the equation d dx (y2) = d dx ( x−1 x1) d d x ( y 2) = d d x ( x 1 x 1) Differentiate the left side of the equation Tap for more steps Ex 94, 12 Find a particular solution satisfying the given condition 𝑥 𝑥2−1 𝑑𝑦𝑑𝑥=1;𝑦=0 When 𝑥=2 𝑥 𝑥2−1 dy = dx dy = 𝑑𝑥𝑥(𝑥2 − 1) Integrating both sides 𝑑𝑦 = 𝑑𝑥𝑥(𝑥2 − 1) 𝑦 = 𝑑𝑥𝑥(𝑥 1)(𝑥 − 1) We can write integrand as 1𝑥(𝑥 1
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Solve your math problems using our free math solver with stepbystep solutions Our math solver supports basic math, prealgebra, algebra, trigonometry, calculus and more Ex 94, 6 For each of the differential equations in Exercises 1 to 10, find the general solution 𝑑𝑦/𝑑𝑥=(1𝑥^2 )(1𝑦^2 ) 𝑑𝑦/𝑑𝑥=(1𝑥^2 )(1𝑦^2 ) dy = (1𝑥^2 )(1𝑦^2 ) dx 𝑑𝑦/(1 𝑦^2 )= (1 𝑥^2) dx Integrating both sides ∫1 𝑑𝑦/(1 𝑦^2 ) = ∫1 (1𝑥2)𝑑𝑥 tan−1 y = x 𝒙^𝟑/𝟑 C If y = (1 1/x^2)/ (1 1/x^2), then dy/dx is Sarthaks eConnect Largest Online Education Community
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This equation is an exact differential dF (x,y) = 0 because P_y = 2y/x^2 = Q_x The solution is F (x,y) = C with F_x = P = 1 y^2/x^2 1/x^2 F_y = Q = 1 2y/x Integrating the second equation leads to F (x,y) = y (y^2)/x G (x) Using the first equation gives G' (x) = 1 1/x^2 so G (x) = x(1 X) (1 Y2) Dx (1 Y) (1 X2) Dy = 0 CBSE CBSE (Science) Class 12 Question Papers 1851 Textbook Solutions MCQ Online Tests 31 Important Solutions 4564 Question Bank Solutions Concept Notes & Videos 725 Time Tables 18 Syllabus Advertisement Remove allImplicit derivative (dy)/ (dx), (xy)^2=xy1 \square!
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Solutionput (xy)=v then differentiate both sides with respect to 'x' we get 1dy/dx=dv/dx or, dy/dx=dv/dx—1 this value put in to equation (I), first arranging equation (I) dy/dx= (xy1) (xy—2)/ (xy2) (xy—1) or, dv/dx—1= (v1) (v—2)/ (v2) (v—1) or,dv/dx= (v^2—2vv—2)/ (v^22v—v—2) 1Find the solution of the differential equation that satisfies the given initial conditiondy/dx = y^2 1, y(1) = 0 Homework Statement rewrite the equation in the form of linear equation Then solve it (1x^2)dy/dx xy = 1/ (1x^2) the ans given is y= x/ (1x^2) C / ( sqrt rt (1x^2) ) , my ans is different , which part is wrong ?
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The issue is that you integrated y with respect to x, and concluded that it was equal to y This is only viable if y = aex for some constant a, which we have no reason to suspect Solve y ^2x (\frac {dy} {dx})^2 = 1 using proposed change of variables Solve y2 −x(dxdy )2 = 1 using proposed change of variablesCalculus Find dy/dx y^2=1/ (1x^2) y2 = 1 1 − x2 y 2 = 1 1 x 2 Differentiate both sides of the equation d dx (y2) = d dx ( 1 1−x2) d d x ( y 2) = d d x ( 1 1 x 2) Differentiate the left side of the equation Tap for more stepsKEAM 11 If y= cot 1( tan (x/2) ), then (dy/dx) is equal to (A) (1/2) (B) 0 (x/2) (D) (1/2) (E) (x/2) Check Answer and Soluti
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(x^2 – y 2) dx (x 2 2xy) dy= 0 Exercise 25 Q1 (xy) dx x dy = 0 Q2 (xy) dx x dy = 0 Q3 x dx (y 2x) dy= 0 Q5 (y 2 yx) dx – x 2 dy = 0 Q11 In Problems 11–14 solve the given initialvalue problem xy 2 dy/dx = y 3 x 3, y(1) = 2 Chapter 3 Exercise 31 Q1 The population of a community is known to increase at a rateTo solve this, let v ( y) = 1 / x ( y) Also, don't forget to pick up both branches of the solution by noting that if y ( x) is a solution, so too is − y ( x) Update Alright, here's how to do it Let v ( y) = 1 / x ( y) Then d x d y = − 1 v ( y) 2 d v d y giving(1) 2/x 2 2/x 3 (2) 2/x 3 1/x 2 (3) 2/x 2 2/x 2 (4) none of these Solution Given y = (1 – x)/x 2 = 1/x 2 – 1/x Differentiate wrtx dy/dx = 2/x 3 – (1/x 2) =
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To ask Unlimited Maths doubts download Doubtnut from https//googl/9WZjCW `(1x^2) dy/dxxy=1` So variable separable method is not possible Now, 𝑑𝑦/𝑑𝑥 = ((1 𝑦^2))/tan^(−1)〖𝑦 − 𝑥〗 Put F(x, y) = 𝑑𝑦/𝑑𝑥 F(x, y) = (1 𝑦^2)/(tan^(−1)𝑦−𝑥) F(𝜆x, 𝜆y) = (1 𝜆^2 𝑦^2)/(tan^(−1)𝜆𝑦−𝜆𝑥)≠ 𝜆° F(x, y) Hence, the equation is not homogenous Solve (1 – x2) (dy/dx) xy = xy2 The given differential equation is Multiplying both sides of Eq (ii) by IF and integrating, we get,
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Experts are tested by Chegg as specialists in their subject area We review their content and use your feedback to keep the quality high 100% (87 ratings) Previous question Next question Transcript Misc 11 Find a particular solution of the differential equation ( )( )= , given that = 1 , when =0 ( = ) ( )( )= y dx y dy = dx dy x dx y dx dxView QUESTION BANK ENG MATHS Ipdf from MATH MA6151 at Rajalakshmi Engineering College QUESTION BANK PART A 1Find dy dx x if y = x 2Find , when y
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Get stepbystep solutions from expert tutors as fast as 1530 minutes Your first 5 questions are on us!√(sec x1/sec x1) A sec2x B 1/2 sec2 x/2 C 1/2 cosec2 x/2 D none of theseSolve the differential equation dy/dx = y/x Solve the differential equation dy/dx = y/x
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6 12 8 4 dy dx 10 x x 2 1 y 3 0 60 4 6 4 6 dy dx 1 12 x 2 y 4 2 61 3 1 3 3 dy dx from TEPSERVER 231 at University of California, San Diego M110 Module 6 Advanced Functions & Logarithms 2 Power & Exponential Functions Questionsdocx y = x 1 C/e^x dy/dx=xy not separable, not exact, so set it up for an integrating factor dy/dx y =x the IF is e^(int dx) = e^x so e^x dy/dx e^x y =xe^x or d/dx (e^x y) =xe^x so e^x y = int xe^x \ dx qquad triangle for the integration, we use IBP int u v' = uv int u' v u = x, u' = 1 v' = e^x, v = e^x implies x e^x int e^x \ dx = x e^x e^x C so going back to triangle e^x y = x e Rewriting the given diff eqn (DE) as #dy/dxy=2x#, we find that it is a linear DE of the form #dy/dxyP(x)=q(x)# To find its gen soln (GS), we need to multiply it by the integrating factor (IF) #e^(intP(x)dx# Since, #P(x)=1, intP(x)dx=int1dx=x " IF is "e^x# Multiplying the DE by IF, we get, #e^xdy/dxye^x=2xe^x#
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To ask Unlimited Maths doubts download Doubtnut from https//googl/9WZjCW `(1x^2)dy/dx=1y^2` dy/dx=x/y x^2y^2=1 Differentiate wrt x d/dxx^2d/dxy^2=d/dx1 We already know how to deal with the first and third terms, so lets get them out the way d/dxx^2d/dxy^2=d/dx1 2xd/dxy^2=0 For the remaining term we use the chain rule, we don't know how to differentiate y^2 wrt x but we do know how to differentiate y^2 wrt y (it the same as differentiating x^2 wrt x!)Calculus Find dy/dx y=1/x y = 1 x y = 1 x Differentiate both sides of the equation d dx (y) = d dx ( 1 x) d d x ( y) = d d x ( 1 x) The derivative of y y with respect to x x is y' y ′ y' y ′ Differentiate the right side of the equation Tap for more steps
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Bernoulli's equation has form, \frac{dy}{dx}p(x)y=q(x)y^n Now, consider this, \frac{dz}{dx}z^2x=z^2z This easily simplifies to, \frac{dz}{dx}z=(1x^2)z^2 where p(x)=1 Find bounded solutions of this ODE https//mathstackexchangecom/questions//findboundedsolutionsofthisode Hint on the first question f(x) = \frac{\sinh(x)}{x} =
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