If y=x (a+y), then d y/d x is : Option 1: ^2 a (a+y) Option 2: (a+y) ^2 a Option 3: (a+y)/ a Option 4: ^2(a+y) a

The answer is '^2(a+y) a'. View full solution:

Calculus > Differential Equations

Medium

core

If $\sin y=x \sin (a+y)$, then $\frac{d y}{d x}$ is :

$\frac{\sin ^{2} a}{\sin (a+y)}$

$\frac{\sin (a+y)}{\sin ^{2} a}$

$\frac{\sin (a+y)}{\sin a}$

$\frac{\sin ^{2}(a+y)}{\sin a}$

✅ Correct Option: 4

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Match List-I with List-II

List-I	List-II
Differential Equation	Order and Degree
(A) $\left(\frac{d^2y}{dx^2}\right)^2 = e^x\left(\frac{dy}{dx}\right)^4 + 1 = 0$	(I) order = 1 and degree = 2
(B) $\left(\frac{dy}{dx}\right)^2 + xy = 0$	(II) order = 2 and degree = 1
(C) $\left(1 + \frac{dy}{dx}\right)^{3/2} = 4\left(\frac{d^2y}{dx^2}\right)^2$	(III) order = 2 and degree = 2
(D) $\sqrt\frac{d^2y}{dx^2} + 1 = \frac{dy}{dx}$	(IV) order = 2 and degree = 4

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$\left(1 + \frac{dy}{dx}\right)^4 = \left(\frac{d^2y}{dx^2}\right)^2$ is: