What is the solution for (dy}{dt}=\frac{4t)/k-0.1yt ?

The solution for (dy}{dt}=\frac{4t)/k-0.1yt is y=-(10e^{(-t^2-c_{1})/(20)})/k+(40)/k

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(dy}{dt}=\frac{4t)/k-0.1yt

\frac{d y}{d t} = \frac{4 t}{k} - 0.1 y t

y = - \frac{10 e ^{\frac{- t ^{2} - c _{1}}{20}}}{k} + \frac{40}{k}

Solution steps

\frac{d y}{d t} = \frac{4 t}{k} - 0.1 y t

Solve separable ODE:

y = - \frac{10 e ^{\frac{- t ^{2} - c _{1}}{20}}}{k} + \frac{40}{k}

y = - \frac{10 e ^{\frac{- t ^{2} - c _{1}}{20}}}{k} + \frac{40}{k}

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What is the solution for (dy}{dt}=\frac{4t)/k-0.1yt ?
The solution for (dy}{dt}=\frac{4t)/k-0.1yt is y=-(10e^{(-t^2-c_{1})/(20)})/k+(40)/k