What is the solution for y^{''}-2y^'+y=4x^2-3+(e^x)/x ?

The solution for y^{''}-2y^'+y=4x^2-3+(e^x)/x is y=c_{1}e^x+c_{2}xe^x+4x^2+16x-e^xx+e^xxln(x)+21

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y^{''}-2y^'+y=4x^2-3+(e^x)/x

y^{^{''}} - 2 y^{^{'}} + y = 4 x^{2} - 3 + \frac{e ^{x}}{x}

y = c_{1} e^{x} + c_{2} x e^{x} + 4 x^{2} + 16 x - e^{x} x + e^{x} x ln (x) + 21

Solution steps

y^{''} (x) - 2 y^{'} (x) + y = 4 x^{2} - 3 + \frac{e ^{x}}{x}

Solve linear ODE:

y = c_{1} e^{x} + c_{2} x e^{x} + 4 x^{2} + 16 x - e^{x} x + e^{x} x ln (x) + 21

y = c_{1} e^{x} + c_{2} x e^{x} + 4 x^{2} + 16 x - e^{x} x + e^{x} x ln (x) + 21

(d^{3} + 4 d) y = e^{x} + sin (x)

2 y^{^{''}} + 18 y^{^{'}} = 6 tan (3 x)

y^{^{''}} - 7 y^{^{'}} + 12 y = e^{3} x + e^{4} x

y^{^{''}} + 4 y^{^{'}} = 10 t + 1

y^{^{''}} + y = cos (x) sec (x)

What is the solution for y^{''}-2y^'+y=4x^2-3+(e^x)/x ?
The solution for y^{''}-2y^'+y=4x^2-3+(e^x)/x is y=c_{1}e^x+c_{2}xe^x+4x^2+16x-e^xx+e^xxln(x)+21