LA

Solve the differential equation $(1+x^{2})\frac{dy}{dx}+2xy-4x^{2}=0$ subject to initial condition $y(0)=0$.

MCQ_SINGLE

Let \(f^{\prime}(x)=3(x^{2}+2x)-\frac{4}{x^{3}}+5,\) and \(f(1)=0\). Then, \(f(x)\) is:

LA

Solve the differential equation $\frac{dy}{dx}=\cos x-2y$.

MCQ_SINGLE

What is the product of the order and degree of the differential equation $\frac{d^{2}y}{dx^{2}}\sin y+(\frac{dy}{dx})^{3}\cos y=\sqrt{y}$ ?

MCQ_SINGLE

If \(p\) and \(q\) are respectively the order and degree of the differential equation \(\frac{d}{dx}(\frac{dy}{dx})^{3}=0,\) then \((p-q)\) is

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