What is the solution for t*(dy)/(dt)=t^3+22t^3y ?

The solution for t*(dy)/(dt)=t^3+22t^3y is y=(e^{(22t^3+c_{1})/3})/(22)-1/22

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t*(dy)/(dt)=t^3+22t^3y

t \cdot \frac{d y}{d t} = t^{3} + 22 t^{3} y

y = \frac{e ^{\frac{22 t ^{3} + c _{1}}{3}}}{22} - \frac{1}{22}

Solution steps

t \cdot \frac{d y}{d t} = t^{3} + 22 t^{3} y

Solve separable ODE:

y = \frac{e ^{\frac{22 t ^{3} + c _{1}}{3}}}{22} - \frac{1}{22}

y = \frac{e ^{\frac{22 t ^{3} + c _{1}}{3}}}{22} - \frac{1}{22}

y = \frac{x}{ln ( x )}

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

\int \frac{1}{4 x - x ^{2}} d x

\frac{d}{d x} (arctan (2 x + 1))

x \to \infty lim (e^{1})

What is the solution for t*(dy)/(dt)=t^3+22t^3y ?
The solution for t*(dy)/(dt)=t^3+22t^3y is y=(e^{(22t^3+c_{1})/3})/(22)-1/22