What is the solution for t*(dy)/(dt)=t^3+9t^3y ?

The solution for t*(dy)/(dt)=t^3+9t^3y is y=(e^{3t^3+c_{1}})/9-1/9

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t*(dy)/(dt)=t^3+9t^3y

t \cdot \frac{d y}{d t} = t^{3} + 9 t^{3} y

y = \frac{e ^{3 t^{3} + c_{1}}}{9} - \frac{1}{9}

Solution steps

t \cdot \frac{d y}{d t} = t^{3} + 9 t^{3} y

Solve separable ODE:

y = \frac{e ^{3 t^{3} + c_{1}}}{9} - \frac{1}{9}

y = \frac{e ^{3 t^{3} + c_{1}}}{9} - \frac{1}{9}

\frac{d}{d x} ((x^{2} + x)^{2} sin^{3} (2 x))

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

\int \frac{1}{x ^{2} + 6 x + 9} d x

x^{3} (x^{2} + 1)^{7}

x^{2} sin^{9} (+ x cos^{- 2} (x))

What is the solution for t*(dy)/(dt)=t^3+9t^3y ?
The solution for t*(dy)/(dt)=t^3+9t^3y is y=(e^{3t^3+c_{1}})/9-1/9