SA

Solve the differential equation $2(y+3)-xy\frac{dy}{dx}=0;$ given $y(1)=-2$.

LA

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

MCQ_SINGLE

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

SA

Find the particular solution of the differential equation $(xe^{\frac{y}{x}}+y)dx=x~dy$, given that $y=1$ when $x=1$

SA

Solve the differential equation given by:$$x \, dy - y \, dx - \sqrt{x^{2} + y^{2}} \, dx = 0$$

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