What is the solution for t*(dy)/(dt)=t^3+25t^3y ?

The solution for t*(dy)/(dt)=t^3+25t^3y is y=(e^{(25t^3+c_{1})/3})/(25)-1/25

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t*(dy)/(dt)=t^3+25t^3y

t \cdot \frac{d y}{d t} = t^{3} + 25 t^{3} y

y = \frac{e ^{\frac{25 t ^{3} + c _{1}}{3}}}{25} - \frac{1}{25}

Solution steps

t \cdot \frac{d y}{d t} = t^{3} + 25 t^{3} y

Solve separable ODE:

y = \frac{e ^{\frac{25 t ^{3} + c _{1}}{3}}}{25} - \frac{1}{25}

y = \frac{e ^{\frac{25 t ^{3} + c _{1}}{3}}}{25} - \frac{1}{25}

\frac{d}{d x} (\frac{e ^{x^{2}}}{x})

y = \frac{2}{3 x ^{3}}

\frac{d y}{d t} = 0.0572 (400 - y)

\int \frac{3 ln ( x + 7 )}{x ^{2}} d x

\frac{1}{3 x ^{2} + 4 x}

What is the solution for t*(dy)/(dt)=t^3+25t^3y ?
The solution for t*(dy)/(dt)=t^3+25t^3y is y=(e^{(25t^3+c_{1})/3})/(25)-1/25