What is the solution for y^'-3/2 y=3t+2e^t ?

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

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y^'-3/2 y=3t+2e^t

y^{^{'}} - \frac{3}{2} y = 3 t + 2 e^{t}

y = - 2 t - \frac{4}{3} - 4 e^{t} + c_{1} e^{\frac{3 t}{2}}

Solution steps

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

Solve linear ODE:

y = - 2 t - \frac{4}{3} - 4 e^{t} + c_{1} e^{\frac{3 t}{2}}

y = - 2 t - \frac{4}{3} - 4 e^{t} + c_{1} e^{\frac{3 t}{2}}

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