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

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

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

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

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

Solution steps

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

Solve separable ODE:

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

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

\frac{d y}{d x} = \frac{y ^{2}}{x}, y (e) = 3

\frac{1}{y} d y = \frac{- x}{1 + x ^{2}} d x

x^{^{'}} = 1 - 3 x + 2 x^{2}

\frac{d y}{d x} = - \frac{x ^{3}}{y ^{3}}

4 y + x \frac{d y}{d x} = 0

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