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

The solution for y^{''}+3/2 y^'=x+e^{2x} is y=c_{1}+c_{2}e^{-(3x)/2}+(x^2)/3-(4x)/9+1/7 e^{2x}

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y^{''}+3/2 y^'=x+e^{2x}

y^{^{''}} + \frac{3}{2} y^{^{'}} = x + e^{2 x}

y = c_{1} + c_{2} e^{- \frac{3 x}{2}} + \frac{x ^{2}}{3} - \frac{4 x}{9} + \frac{1}{7} e^{2 x}

Solution steps

y^{''} (x) + \frac{3}{2} y^{'} (x) = x + e^{2 x}

Solve linear ODE:

y = c_{1} + c_{2} e^{- \frac{3 x}{2}} + \frac{x ^{2}}{3} - \frac{4 x}{9} + \frac{1}{7} e^{2 x}

y = c_{1} + c_{2} e^{- \frac{3 x}{2}} + \frac{x ^{2}}{3} - \frac{4 x}{9} + \frac{1}{7} e^{2 x}

What is the solution for y^{''}+3/2 y^'=x+e^{2x} ?
The solution for y^{''}+3/2 y^'=x+e^{2x} is y=c_{1}+c_{2}e^{-(3x)/2}+(x^2)/3-(4x)/9+1/7 e^{2x}