Pls me solve the questions in d pdf

I'll take a stab at what I think is the most interesting problem in the attachment.


Substitute and , so that and . Then the ODE becomes



We would like to have this be a homogeneous equation, which is to say, given



there is some for which . In order for this to be true, we require that the constant terms in the numerator and denominator vanish. That is,



which is easy to solve; you'd find that and . Now, the ODE is



Substitute , so that , and the ODE is





which is separable. You have



and integrating both sides is easy. Substituting , so that , you have