The solution of the differential equation dy/dx = ^2/(x+y)^2 ( is constant) is: Option 1: y = -^2/x+y + C Option 2: (x+y)^3/3 = ^2 x + C Option 3: ^-1(x+y/) = y + C Option 4: y = -2^2/(x+y)^3 + C

The answer is '^-1(x+y/) = y + C'. View full solution:

CUET Mathematics - The solution of the differential equation dy/dx = ^2/(x+y)^2 ( is constant) is: | PYQs + Solutions

CUET Mathematics 2022 4 Aug Shift 1

Calculus

Hard

$y = \frac{-\lambda^2}{x+y} + C$

$\frac{(x+y)^3}{3} = \lambda^2 x + C$

$\lambda \tan^{-1}\left(\frac{x+y}{\lambda}\right) = y + C$

$y = \frac{-2\lambda^2}{(x+y)^3} + C$

✅ Correct Option: 3

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General solution of the differential equation $\frac{dy}{dx} + \frac{\sqrt{1 - y^2}}{\sqrt{1 - x^2}} = 0$ is

A. $\tan^{-1} x + \tan^{-1} y = C$

B. $\sin^{-1} x - \cos^{-1} y = C$

C. $x\sqrt{1 - y^2} - y\sqrt{1 - x^2} = C$

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E. $\cos^{-1} x + \cos^{-1} y = C$

(where C is arbitrary constant)

Choose the correct answer from the options given below