What is the solution for t(dy)/(dt)=y+4t^2sin(3t) ?

The solution for t(dy)/(dt)=y+4t^2sin(3t) is y=-4/3 cos(3t)t+c_{1}t

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t(dy)/(dt)=y+4t^2sin(3t)

t \frac{d y}{d t} = y + 4 t^{2} sin (3 t)

y = - \frac{4}{3} cos (3 t) t + c_{1} t

Solution steps

t \frac{d y}{d t} = y + 4 t^{2} sin (3 t)

Solve linear ODE:

y = - \frac{4}{3} cos (3 t) t + c_{1} t

y = - \frac{4}{3} cos (3 t) t + c_{1} t

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

- 2 sin (t) cos (t)

x^{x}, 1

\frac{d}{d x} ((x^{2} + y^{2} + z^{2})^{- \frac{1}{2}})

\int \frac{1}{( x ^{2} - 100 ) ^{2}} d x

What is the solution for t(dy)/(dt)=y+4t^2sin(3t) ?
The solution for t(dy)/(dt)=y+4t^2sin(3t) is y=-4/3 cos(3t)t+c_{1}t