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

The solution for y^{''}-y^'-5y=5t+7 is y=c_{1}e^{((1+sqrt(21))t)/2}+c_{2}e^{((1-sqrt(21))t)/2}-t-6/5

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

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

y = c_{1} e^{\frac{( 1 + 21 ) t}{2}} + c_{2} e^{\frac{( 1 - 21 ) t}{2}} - t - \frac{6}{5}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{\frac{( 1 + 21 ) t}{2}} + c_{2} e^{\frac{( 1 - 21 ) t}{2}} - t - \frac{6}{5}

y = c_{1} e^{\frac{( 1 + 21 ) t}{2}} + c_{2} e^{\frac{( 1 - 21 ) t}{2}} - t - \frac{6}{5}

y^{^{''}} + 3 y = - 48 x e^{3 x}

y^{^{''}} + 8 y^{^{'}} + 8 y = cos (4 x)

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

x^{^{''}} + 6 x^{^{'}} + 34 x = 68

y^{^{''}} - 5 y^{^{'}} + 6 y = 2 x^{2} - 1

What is the solution for y^{''}-y^'-5y=5t+7 ?
The solution for y^{''}-y^'-5y=5t+7 is y=c_{1}e^{((1+sqrt(21))t)/2}+c_{2}e^{((1-sqrt(21))t)/2}-t-6/5