Solve $(t^2+3ty+y^2)-t^2y'=0, y(1)=0$, for $t>0$ $(t^2+3ty+y^2)-t^2y'=0, y(1)=0$, for $t>0$.
$$\frac{\frac{\partial M}{\partial y}-\frac{\partial N}{\partial t}}{N}=\frac{5t+2y}{-t^2}$$which is not a function of t only. Then I am stuck. Could anyone help? Thanks

Note that the equation becomes:
$$y' = \frac{t^2 + 3ty + y^2}{t^2}$$
which is a homogeneous ODE. Now substitute $y=ut$ to reduce it to an equation which can be easily solved.
