What is the solution for t*(dy)/(dt)=t^3+30t^3y ?

The solution for t*(dy)/(dt)=t^3+30t^3y is y=(e^{10t^3+c_{1}})/(30)-1/30

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t*(dy)/(dt)=t^3+30t^3y

t \cdot \frac{d y}{d t} = t^{3} + 30 t^{3} y

y = \frac{e ^{10 t^{3} + c_{1}}}{30} - \frac{1}{30}

Solution steps

t \cdot \frac{d y}{d t} = t^{3} + 30 t^{3} y

Solve separable ODE:

y = \frac{e ^{10 t^{3} + c_{1}}}{30} - \frac{1}{30}

y = \frac{e ^{10 t^{3} + c_{1}}}{30} - \frac{1}{30}

n = 0 \sum \infty n! (x - 3)^{n}

f (x) = 2 x^{\frac{1}{3}} + \frac{x}{3} - \frac{1}{4} x^{3}

\int - 7 (- 7 x)^{3} d x

\frac{d}{d x} (x^{4} e^{9 x})

\frac{d}{d x} (\frac{6}{7 x ^{4}})

What is the solution for t*(dy)/(dt)=t^3+30t^3y ?
The solution for t*(dy)/(dt)=t^3+30t^3y is y=(e^{10t^3+c_{1}})/(30)-1/30