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

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

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x^2(dy)/(dx)+x(x+2)y=e^x

x^{2} \frac{d y}{d x} + x (x + 2) y = e^{x}

y = \frac{e ^{x}}{2 x ^{2}} + \frac{c _{1}}{e ^{x} x ^{2}}

Solution steps

x^{2} \frac{d y}{d x} + x (x + 2) y = e^{x}

Solve linear ODE:

y = \frac{e ^{x}}{2 x ^{2}} + \frac{c _{1}}{e ^{x} x ^{2}}

y = \frac{e ^{x}}{2 x ^{2}} + \frac{c _{1}}{e ^{x} x ^{2}}

\int \frac{7}{( x - 3 ) ( x + 4 )} d x

e^{- \frac{t}{4}}

t \to 1 lim (e^{4 t})

\frac{d y}{d x} - 4 y = x^{6} e^{x}

y = 5 x e^{x} csc (x)

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