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

The solution for y^{''}-2y^'+y=x(cosh(x)) is y=c_{1}e^x+c_{2}xe^x+(2e^xx^3+3e^{-x}x+3e^{-x})/(24)

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

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

y = c_{1} e^{x} + c_{2} x e^{x} + \frac{2 e ^{x} x ^{3} + 3 e ^{- x} x + 3 e ^{- x}}{24}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{x} + c_{2} x e^{x} + \frac{2 e ^{x} x ^{3} + 3 e ^{- x} x + 3 e ^{- x}}{24}

y = c_{1} e^{x} + c_{2} x e^{x} + \frac{2 e ^{x} x ^{3} + 3 e ^{- x} x + 3 e ^{- x}}{24}

What is the solution for y^{''}-2y^'+y=x(cosh(x)) ?
The solution for y^{''}-2y^'+y=x(cosh(x)) is y=c_{1}e^x+c_{2}xe^x+(2e^xx^3+3e^{-x}x+3e^{-x})/(24)