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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

\frac{\partial}{\partial x} (x^{2} - 4 x y + 4 y^{2} + 2)

x, 1, \frac{x ^{2}}{4}

y = \frac{cos ( x )}{x ^{3}}

y = 600 - \frac{x ^{2}}{121}

x^{^{'}} = x - x^{2}

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