What is the solution for y^{''}-7y^'=5x-3 ?

The solution for y^{''}-7y^'=5x-3 is y=c_{1}e^{7x}+c_{2}-(5x^2)/(14)+(16x)/(49)

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y^{''}-7y^'=5x-3

y^{^{''}} - 7 y^{^{'}} = 5 x - 3

y = c_{1} e^{7 x} + c_{2} - \frac{5 x ^{2}}{14} + \frac{16 x}{49}

Solution steps

y^{''} (x) - 7 y^{'} (x) = 5 x - 3

Solve linear ODE:

y = c_{1} e^{7 x} + c_{2} - \frac{5 x ^{2}}{14} + \frac{16 x}{49}

y = c_{1} e^{7 x} + c_{2} - \frac{5 x ^{2}}{14} + \frac{16 x}{49}

y^{^{''}} - 2 y^{^{'}} + 50 y = e^{x} cos (7 x)

\frac{d ^{2} y}{d x ^{2}} - y = e^{x}

y^{^{''}} + 25 y^{^{'}} = - 24 t e^{- t}

y^{^{''}} + 4 y^{^{'}} + y = (\frac{e ^{- \frac{x}{2}}}{x ^{2}})

2 y^{^{''}} - 2 y^{^{'}} - 4 y = 2 e^{3 t}

What is the solution for y^{''}-7y^'=5x-3 ?
The solution for y^{''}-7y^'=5x-3 is y=c_{1}e^{7x}+c_{2}-(5x^2)/(14)+(16x)/(49)