Question

Find all the solutions of the Differential Equation
dy/dt - 2y^2 = ty^2

Answer 1

I would say start with separating your variables. (all your y's on one side and the t's on the other)

Answer 2

After that take an integral.

Answer 3

that helps, thanks.

Answer 4

\[y'[t]-2 y^2=t y^2\to y'[t]=t y^2+2 y^2 \]
\[\int\limits y'[t] \, dt=\int\limits \left(-2 y^2+t y^2\right) \, dt \]
\[y[t]=-2 t y^2+\frac{t^2 y^2}{2} \]