What is the solution for 5y^{''}+10y^'=3x^2 ?

The solution for 5y^{''}+10y^'=3x^2 is y=c_{1}+c_{2}e^{-2x}+(x^3)/(10)-(3x^2)/(20)+(3x)/(20)

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5y^{''}+10y^'=3x^2

5 y^{^{''}} + 10 y^{^{'}} = 3 x^{2}

y = c_{1} + c_{2} e^{- 2 x} + \frac{x ^{3}}{10} - \frac{3 x ^{2}}{20} + \frac{3 x}{20}

Solution steps

5 y^{''} (x) + 10 y^{'} (x) = 3 x^{2}

Solve linear ODE:

y = c_{1} + c_{2} e^{- 2 x} + \frac{x ^{3}}{10} - \frac{3 x ^{2}}{20} + \frac{3 x}{20}

y = c_{1} + c_{2} e^{- 2 x} + \frac{x ^{3}}{10} - \frac{3 x ^{2}}{20} + \frac{3 x}{20}

What is the solution for 5y^{''}+10y^'=3x^2 ?
The solution for 5y^{''}+10y^'=3x^2 is y=c_{1}+c_{2}e^{-2x}+(x^3)/(10)-(3x^2)/(20)+(3x)/(20)