What is the solution for linear y^{''}+5y^'=15x^2 ?

The solution for linear y^{''}+5y^'=15x^2 is y=c_{1}+c_{2}e^{-5x}+x^3-(3x^2)/5+(6x)/(25)

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linear y^{''}+5y^'=15x^2

linear

y^{^{''}} + 5 y^{^{'}} = 15 x^{2}

y = c_{1} + c_{2} e^{- 5 x} + x^{3} - \frac{3 x ^{2}}{5} + \frac{6 x}{25}

Solution steps

y^{''} (x) + 5 y^{'} (x) = 15 x^{2}

Solve linear ODE:

y = c_{1} + c_{2} e^{- 5 x} + x^{3} - \frac{3 x ^{2}}{5} + \frac{6 x}{25}

y = c_{1} + c_{2} e^{- 5 x} + x^{3} - \frac{3 x ^{2}}{5} + \frac{6 x}{25}

What is the solution for linear y^{''}+5y^'=15x^2 ?
The solution for linear y^{''}+5y^'=15x^2 is y=c_{1}+c_{2}e^{-5x}+x^3-(3x^2)/5+(6x)/(25)