What is the solution for y^{''}-2y^'+y=-1/(x^2)e^x ?

The solution for y^{''}-2y^'+y=-1/(x^2)e^x is y=c_{1}e^x+c_{2}xe^x+e^xln(x)+e^x

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y^{''}-2y^'+y=-1/(x^2)e^x

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

y = c_{1} e^{x} + c_{2} x e^{x} + e^{x} ln (x) + e^{x}

Solution steps

y^{''} (x) - 2 y^{'} (x) + y = - \frac{1}{x ^{2}} e^{x}

Solve linear ODE:

y = c_{1} e^{x} + c_{2} x e^{x} + e^{x} ln (x) + e^{x}

y = c_{1} e^{x} + c_{2} x e^{x} + e^{x} ln (x) + e^{x}

y^{^{''}} + \frac{1}{8} y^{^{'}} + 4 y = 3 cos (6 t)

y^{^{''}} + 7 y^{^{'}} + 12 y = 21 e^{3 t}

y^{^{''}} + 3^{2} y = 6 \cdot sin (3 x)

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} + 5 y = x e^{2 x}

y^{^{''}} - 2 y^{^{'}} + y = x^{3} + 3 x

What is the solution for y^{''}-2y^'+y=-1/(x^2)e^x ?
The solution for y^{''}-2y^'+y=-1/(x^2)e^x is y=c_{1}e^x+c_{2}xe^x+e^xln(x)+e^x