What is the solution for (dy)/(dt)= y/2+4e^{t/2} ?

The solution for (dy)/(dt)= y/2+4e^{t/2} is y=4e^{t/2}t+c_{1}e^{t/2}

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(dy)/(dt)= y/2+4e^{t/2}

\frac{d y}{d t} = \frac{y}{2} + 4 e^{\frac{t}{2}}

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

Solution steps

\frac{d y}{d t} = \frac{y}{2} + 4 e^{\frac{t}{2}}

Solve linear ODE:

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

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

What is the solution for (dy)/(dt)= y/2+4e^{t/2} ?
The solution for (dy)/(dt)= y/2+4e^{t/2} is y=4e^{t/2}t+c_{1}e^{t/2}