What is the solution for y^{''}+5y^'+4y=8x^2 ?

The solution for y^{''}+5y^'+4y=8x^2 is y=c_{1}e^{-x}+c_{2}e^{-4x}+2x^2-5x+21/4

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y^{''}+5y^'+4y=8x^2

y^{^{''}} + 5 y^{^{'}} + 4 y = 8 x^{2}

y = c_{1} e^{- x} + c_{2} e^{- 4 x} + 2 x^{2} - 5 x + \frac{21}{4}

Solution steps

y^{''} (x) + 5 y^{'} (x) + 4 y = 8 x^{2}

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} e^{- 4 x} + 2 x^{2} - 5 x + \frac{21}{4}

y = c_{1} e^{- x} + c_{2} e^{- 4 x} + 2 x^{2} - 5 x + \frac{21}{4}

x y^{^{''}} + 3 y^{^{'}} = 1984 (x^{19})^{82}

\int \frac{10800 x}{9 x ^{2} + 675} d x

\frac{d}{d x} (sin (x^{2} + e^{x}))

f (x) = \frac{5 x ^{4} - 3 x ^{3}}{x ^{5}}

(\frac{x - 1}{x + 1})^{^{'}}

What is the solution for y^{''}+5y^'+4y=8x^2 ?
The solution for y^{''}+5y^'+4y=8x^2 is y=c_{1}e^{-x}+c_{2}e^{-4x}+2x^2-5x+21/4