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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

(11 x y^{2} - 13 y) + (11 x^{2} y - 13 x) \cdot \frac{d y}{d x} = 0

x \to + (- 1) lim (- x^{2} + 4 x - 5)

\frac{d y}{d x} = 4 x 1 - y^{2}

\int (1 - cos (x)) d x

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