What is the solution for (dy)/(dt)+0.5ty-4t=0 ?

The solution for (dy)/(dt)+0.5ty-4t=0 is y=2e^{c_{1}-(t^2)/4}+8

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(dy)/(dt)+0.5ty-4t=0

\frac{d y}{d t} + 0.5 t y - 4 t = 0

y = 2 e^{c_{1} - \frac{t ^{2}}{4}} + 8

Solution steps

\frac{d y}{d t} + 0.5 t y - 4 t = 0

Solve separable ODE:

y = 2 e^{c_{1} - \frac{t ^{2}}{4}} + 8

y = 2 e^{c_{1} - \frac{t ^{2}}{4}} + 8

What is the solution for (dy)/(dt)+0.5ty-4t=0 ?
The solution for (dy)/(dt)+0.5ty-4t=0 is y=2e^{c_{1}-(t^2)/4}+8