How do you solve this differential equation t^2dy/dx+y^2=ty

If is just a constant, then you have a fairly simple (separable) ODE.



and so on.

So, I'll assume you meant to write ...



This is a standard Bernoulli equation, which means a substitution of will suffice to transform this ODE in into a linear ODE in . You have




which changes the ODE to




An integrating factor would be



Multiplying both sides by the IF gives




Integrate both sides wrt to get




Now back substitute. Since , you get and the solution is