What is the solution for y^{''}-2y^'+y=x^3+5x ?

The solution for y^{''}-2y^'+y=x^3+5x is y=c_{1}e^x+c_{2}xe^x+x^3+6x^2+23x+34

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y^{''}-2y^'+y=x^3+5x

y^{^{''}} - 2 y^{^{'}} + y = x^{3} + 5 x

y = c_{1} e^{x} + c_{2} x e^{x} + x^{3} + 6 x^{2} + 23 x + 34

Solution steps

y^{''} (x) - 2 y^{'} (x) + y = x^{3} + 5 x

Solve linear ODE:

y = c_{1} e^{x} + c_{2} x e^{x} + x^{3} + 6 x^{2} + 23 x + 34

y = c_{1} e^{x} + c_{2} x e^{x} + x^{3} + 6 x^{2} + 23 x + 34

y^{^{''}} - 2 y^{^{'}} + y = \frac{e ^{x}}{x} + e^{x} x^{2} + 5 cos (2 x)

y^{^{''}} - 2 y^{^{'}} + 2 y = 2 x - 2, y^{^{'}} (π) = π, y (0) = 0

\frac{d ^{2} y}{d x ^{2}} + 4 y = sin^{2} (x)

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

y^{^{''}} + 7 y^{^{'}} + 6 y = 24

What is the solution for y^{''}-2y^'+y=x^3+5x ?
The solution for y^{''}-2y^'+y=x^3+5x is y=c_{1}e^x+c_{2}xe^x+x^3+6x^2+23x+34