What is the solution for y^{''}-4y^'-5y=2cosh(x) ?

The solution for y^{''}-4y^'-5y=2cosh(x) is y=c_{1}e^{5x}+c_{2}e^{-x}+(-12e^{-x}x-2e^{-x}-9e^x)/(72)

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y^{''}-4y^'-5y=2cosh(x)

y^{^{''}} - 4 y^{^{'}} - 5 y = 2 cosh (x)

y = c_{1} e^{5 x} + c_{2} e^{- x} + \frac{- 12 e ^{- x} x - 2 e ^{- x} - 9 e ^{x}}{72}

Solution steps

y^{''} (x) - 4 y^{'} (x) - 5 y = 2 cosh (x)

Solve linear ODE:

y = c_{1} e^{5 x} + c_{2} e^{- x} + \frac{- 12 e ^{- x} x - 2 e ^{- x} - 9 e ^{x}}{72}

y = c_{1} e^{5 x} + c_{2} e^{- x} + \frac{- 12 e ^{- x} x - 2 e ^{- x} - 9 e ^{x}}{72}

(d^{2} - 4 d + 4) y = 8 x^{2} e^{2} x sin^{2} (x)

(d^{3} - 6 d^{2} + 11 d - 6) y = e - 2 x + e - 3 x

(d^{2} + 4) y = sin^{3} (x)

(d - 4) y = x^{2}

(d^{2} - 2 d) y = x^{3}

What is the solution for y^{''}-4y^'-5y=2cosh(x) ?
The solution for y^{''}-4y^'-5y=2cosh(x) is y=c_{1}e^{5x}+c_{2}e^{-x}+(-12e^{-x}x-2e^{-x}-9e^x)/(72)