Greetings, I have a few differential equation questions and I began to take this course at the beginning of this semester so I might have been doing obvious mistakes.These questions are from Ross,Differential Equations1st edition chapter 2.2.

3.

14.

23.(a)Prove that if is a homogeneous equation, then the change of variables transforms this equation into a separable equation in the variables u and x.

(b)Use this result to solve

(c)Use this result to solve

In Q3 I found and unable to reduce this expresion to as given in the answers at the back of the book. In Q14 I got the following expression and unable to proceed further:

where .

In Q23 I started with then letting x=uy leads

It follows that:

Is the aforementioned approach right or wrong?

Any help is appreciated,

Thanks in advance.