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 \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 \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}

\int (y sin (x y)) d x

\frac{\partial}{\partial x} (y^{2} - 4 x^{2} + 7 y + 5 x + 13)

y^{^{'}} + 5 (cos (5 x)) y = - 8 cos (5 x)

y^{2} = 4 x, y^{2} = 8 x - 4, x

x \to 42 lim (\frac{x ^{2}}{6} - \frac{7}{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