What is the solution for y^{''}-5y^'=3e^{5t}-7t+4 ?

The solution for y^{''}-5y^'=3e^{5t}-7t+4 is y=c_{1}e^{5t}+c_{2}+(3e^{5t}t)/5+(7t^2)/(10)-(13t)/(25)

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y^{''}-5y^'=3e^{5t}-7t+4

y^{^{''}} - 5 y^{^{'}} = 3 e^{5 t} - 7 t + 4

y = c_{1} e^{5 t} + c_{2} + \frac{3 e ^{5 t} t}{5} + \frac{7 t ^{2}}{10} - \frac{13 t}{25}

Solution steps

y^{''} (t) - 5 y^{'} (t) = 3 e^{5 t} - 7 t + 4

Solve linear ODE:

y = c_{1} e^{5 t} + c_{2} + \frac{3 e ^{5 t} t}{5} + \frac{7 t ^{2}}{10} - \frac{13 t}{25}

y = c_{1} e^{5 t} + c_{2} + \frac{3 e ^{5 t} t}{5} + \frac{7 t ^{2}}{10} - \frac{13 t}{25}

What is the solution for y^{''}-5y^'=3e^{5t}-7t+4 ?
The solution for y^{''}-5y^'=3e^{5t}-7t+4 is y=c_{1}e^{5t}+c_{2}+(3e^{5t}t)/5+(7t^2)/(10)-(13t)/(25)