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

The solution for 2y^{''}-5y^'+2y=5x^4cosh(x) is

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

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

y = c_{1} e^{2 x} + c_{2} e^{\frac{x}{2}} + e^{2 x} \cdot \int \frac{5 x ^{4} cosh ( x )}{3 e ^{2 x}} d x + e^{\frac{x}{2}} \cdot \int - \frac{5 x ^{4} cosh ( x )}{3 e ^{\frac{x}{2}}} d x

Solution steps

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

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{\frac{x}{2}} + e^{2 x} \cdot \int \frac{5 x ^{4} cosh ( x )}{3 e ^{2 x}} d x + e^{\frac{x}{2}} \cdot \int - \frac{5 x ^{4} cosh ( x )}{3 e ^{\frac{x}{2}}} d x

y = c_{1} e^{2 x} + c_{2} e^{\frac{x}{2}} + e^{2 x} \cdot \int \frac{5 x ^{4} cosh ( x )}{3 e ^{2 x}} d x + e^{\frac{x}{2}} \cdot \int - \frac{5 x ^{4} cosh ( x )}{3 e ^{\frac{x}{2}}} d x

y^{^{''''}} - y = 14 t + cos (t)

y^{^{''}} + y = - x^{- 2} sin (x) + 2 x^{- 1} cos (x)

y^{^{''}} + y = sin (x) sin (2 x)

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

y^{^{''}} + 2 y^{^{'}} + 10 y = 17 sin (x) - 37 sin (3 x)

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