How Do You Solve a Differential Equation for Different Values of Parameter a?

[Bassalisk]

Homework Statement

Find all functions y=y(x) for all values of parameter a that satisfy differential equation:
[PLAIN]http://pokit.etf.ba/get/5f2923b6e770cea2b31afe7adfc2d998.jpg

Homework Equations

The Attempt at a Solution

Hello,

I was given this equation to solve for my courseware. Now the problem is, I am not very familiar with this type of equation. I assume you equalize 2 parts with zero. But when you find all solutions for both parts what do you do?

Also, I was told that this equation is hard because you need to discuss for different values of a, solutions.

Can anybody here help me solve this equation?

 

[tiny-tim]

Hello Bassalisk!

… I assume you equalize 2 parts with zero. But when you find all solutions for both parts what do you do?

Yes, y satisfies the whole equation if it satisfies either of the two parts.

The set of solutions is the union of the two sets of solutions …

ie, you don't add them or do anything like that, you just list them, and combine the lists.

Also, I was told that this equation is hard because you need to discuss for different values of a, solutions.

Try it and see!