What is the solution for x(dy)/(dx)-2y=x^{-2}+2x^3e^x ?

The solution for x(dy)/(dx)-2y=x^{-2}+2x^3e^x is y=-1/(4x^2)+2e^xx^2+c_{1}x^2

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x(dy)/(dx)-2y=x^{-2}+2x^3e^x

x \frac{d y}{d x} - 2 y = x^{- 2} + 2 x^{3} e^{x}

y = - \frac{1}{4 x ^{2}} + 2 e^{x} x^{2} + c_{1} x^{2}

Solution steps

x \frac{d y}{d x} - 2 y = x^{- 2} + 2 x^{3} e^{x}

Solve linear ODE:

y = - \frac{1}{4 x ^{2}} + 2 e^{x} x^{2} + c_{1} x^{2}

y = - \frac{1}{4 x ^{2}} + 2 e^{x} x^{2} + c_{1} x^{2}

\int \frac{e ^{x}}{5 + e ^{2 x}} d x

\frac{d}{d x} (\frac{1}{2} (sin (x) + x cos (x)))

\frac{d}{d x} (cot (3 x^{2} - 8))

x \to 5 lim (e^{6})

n = 0 \sum \infty \frac{1}{( 2 n + 1 ) ^{2}}

What is the solution for x(dy)/(dx)-2y=x^{-2}+2x^3e^x ?
The solution for x(dy)/(dx)-2y=x^{-2}+2x^3e^x is y=-1/(4x^2)+2e^xx^2+c_{1}x^2