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

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

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

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

y = - e^{2 t} t - e^{2 t} + c_{1} e^{3 t}

Solution steps

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

Solve linear ODE:

y = - e^{2 t} t - e^{2 t} + c_{1} e^{3 t}

y = - e^{2 t} t - e^{2 t} + c_{1} e^{3 t}

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