What is the solution for y^{''}-2y^'-3y=-9te-t ?

The solution for y^{''}-2y^'-3y=-9te-t is y=c_{1}e^{3t}+c_{2}e^{-t}+((9e+1)t)/3-(2(9e+1))/9

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y^{''}-2y^'-3y=-9te-t

y^{^{''}} - 2 y^{^{'}} - 3 y = - 9 t e - t

y = c_{1} e^{3 t} + c_{2} e^{- t} + \frac{( 9 e + 1 ) t}{3} - \frac{2 ( 9 e + 1 )}{9}

Solution steps

y^{''} (t) - 2 y^{'} (t) - 3 y = - 9 t e - t

Solve linear ODE:

y = c_{1} e^{3 t} + c_{2} e^{- t} + \frac{( 9 e + 1 ) t}{3} - \frac{2 ( 9 e + 1 )}{9}

y = c_{1} e^{3 t} + c_{2} e^{- t} + \frac{( 9 e + 1 ) t}{3} - \frac{2 ( 9 e + 1 )}{9}

What is the solution for y^{''}-2y^'-3y=-9te-t ?
The solution for y^{''}-2y^'-3y=-9te-t is y=c_{1}e^{3t}+c_{2}e^{-t}+((9e+1)t)/3-(2(9e+1))/9