What is the solution for y^{''}-2y^'+y=-6-3x+(2e^x)/x ?

The solution for y^{''}-2y^'+y=-6-3x+(2e^x)/x is y=c_{1}e^x+c_{2}xe^x-3x-2e^xx+2e^xxln(x)-12

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y^{''}-2y^'+y=-6-3x+(2e^x)/x

y^{^{''}} - 2 y^{^{'}} + y = - 6 - 3 x + \frac{2 e ^{x}}{x}

y = c_{1} e^{x} + c_{2} x e^{x} - 3 x - 2 e^{x} x + 2 e^{x} x ln (x) - 12

Solution steps

y^{''} (x) - 2 y^{'} (x) + y = - 6 - 3 x + \frac{2 e ^{x}}{x}

Solve linear ODE:

y = c_{1} e^{x} + c_{2} x e^{x} - 3 x - 2 e^{x} x + 2 e^{x} x ln (x) - 12

y = c_{1} e^{x} + c_{2} x e^{x} - 3 x - 2 e^{x} x + 2 e^{x} x ln (x) - 12

\frac{d}{d x} (ln (x^{2} e^{x^{2 + 1}}))

\int cot^{5} (x) csc^{2} (x) d x

\int_{2}^{5} t^{4} ln (2 t) d t

x \to 0 lim ((1 + \frac{4}{x ^{4}})^{x})

(\frac{- 9 x ^{2} + 12 x + 24}{( x ^{2} - 5 x - 6 ) ^{2}})^{^{'}}

What is the solution for y^{''}-2y^'+y=-6-3x+(2e^x)/x ?
The solution for y^{''}-2y^'+y=-6-3x+(2e^x)/x is y=c_{1}e^x+c_{2}xe^x-3x-2e^xx+2e^xxln(x)-12