LA

If $x = \cos t, y = \cos mt$, prove that $\left(1-x^2\right) \frac{d^2y}{dx^2} - x \frac{dy}{dx} + m^2y = 0$.

MCQ_SINGLE

The integrating factor of the differential equation \((\frac{e^{-2\sqrt{x}}}{\sqrt{x}}-\frac{y}{\sqrt{x}})\frac{dx}{dy}=1\) is:

MCQ_SINGLE

The integrating factor of the differential equation \((1-x^{2})\frac{dy}{dx}+xy=ax,\) \(-1 \lt x\lt 1\) is:

MCQ_SINGLE

11. The order and degree (if defined) of the differential equation, $(\frac{d^{2}y}{dx^{2}})^{2}+(\frac{dy}{dx})^{2}=x\sin(\frac{dy}{dx})$ respectively are :

MCQ_SINGLE

The differential equation \(\frac{dy}{dx}=F(x,y)\) will not be a homogeneous differential equation, if \(F(x,y)\) is :

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