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

The solution for y^{''}-7y^'=5t is y=c_{1}e^{7t}+c_{2}-(5t^2)/(14)-(5t)/(49)

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y^{''}-7y^'=5t

y^{^{''}} - 7 y^{^{'}} = 5 t

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

Solution steps

y^{''} (t) - 7 y^{'} (t) = 5 t

Solve linear ODE:

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

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

What is the solution for y^{''}-7y^'=5t ?
The solution for y^{''}-7y^'=5t is y=c_{1}e^{7t}+c_{2}-(5t^2)/(14)-(5t)/(49)