What is the solution for (dy)/(dt)-y/(2t)=3t ?

The solution for (dy)/(dt)-y/(2t)=3t is y=2t^{3/2}sqrt(t)+c_{1}sqrt(t)

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(dy)/(dt)-y/(2t)=3t

\frac{d y}{d t} - \frac{y}{2 t} = 3 t

y = 2 t^{\frac{3}{2}} t + c_{1} t

Solution steps

\frac{d y}{d t} - \frac{y}{2 t} = 3 t

Solve linear ODE:

y = 2 t^{\frac{3}{2}} t + c_{1} t

y = 2 t^{\frac{3}{2}} t + c_{1} t

x \to 0 lim (ln (x^{2}) - x^{- 2})

\frac{d}{d x} ((x^{3} - 9 x)^{- \frac{1}{3}})

\frac{d}{d x} (tan (cot (ln (x))) + sec (e^{x}))

x \to 0 + lim (\frac{sin ( x )}{x})

\frac{\partial}{\partial x} (x^{3} y z^{2} + 4 yz)

What is the solution for (dy)/(dt)-y/(2t)=3t ?
The solution for (dy)/(dt)-y/(2t)=3t is y=2t^{3/2}sqrt(t)+c_{1}sqrt(t)