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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

\int 4 - y d y

x^{2} + y^{2} = 49

y^{^{''}} + 4 y = 3 sin (2 t), y (0) = 2, y^{^{'}} (0) = - 1

\frac{d}{d x} (\frac{x - 3 x x}{x})

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

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