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}}

y^{^{''''}} - y^{^{''}} + y = 0

2 y^{^{''}} - 7 y^{^{'}} - 15 y = 0, y (0) = 2, y^{^{'}} (0) = 1

f (x) = x^{3} + 6 x^{2} + x df (x)

\frac{d}{d x} (3 x + 4 y)

\int \frac{30}{( 1 - x ^{2} ) ^{\frac{3}{2}}} d x

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}