What is the solution for (ydy)/(dt)=(1+y^2)t^2 ?

The solution for (ydy)/(dt)=(1+y^2)t^2 is y=sqrt(e^{(2t^3)/3+c_{1)}-1},y=-sqrt(e^{(2t^3)/3+c_{1)}-1}

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(ydy)/(dt)=(1+y^2)t^2

\frac{y d y}{d t} = (1 + y^{2}) t^{2}

y = e^{\frac{2 t ^{3}}{3} + c_{1}} - 1, y = - e^{\frac{2 t ^{3}}{3} + c_{1}} - 1

Solution steps

\frac{y d y}{d t} = (1 + y^{2}) t^{2}

Solve separable ODE:

y = e^{\frac{2 t ^{3}}{3} + c_{1}} - 1, y = - e^{\frac{2 t ^{3}}{3} + c_{1}} - 1

y = e^{\frac{2 t ^{3}}{3} + c_{1}} - 1, y = - e^{\frac{2 t ^{3}}{3} + c_{1}} - 1

(t + 2) y^{^{'}} + y = (\frac{1}{t - 1})

x \to 5 - lim (5 - x)

\frac{\partial}{\partial z} (4 x^{3} + z^{2})

7 x^{4}

x, x, x = 0, x = 2

What is the solution for (ydy)/(dt)=(1+y^2)t^2 ?
The solution for (ydy)/(dt)=(1+y^2)t^2 is y=sqrt(e^{(2t^3)/3+c_{1)}-1},y=-sqrt(e^{(2t^3)/3+c_{1)}-1}