Differential Equations Question

[MeMoses]

Homework Statement

Match each of the differential equations with a solution from the list below.
1. 2x^2 * y'' + 3xy' = y
2. y'' + 12y' + 36y = 0
3. y'' - 12y' + 36y = 0
4. y'' + y = 0

And then the possible solutions A-D

Homework Equations

The Attempt at a Solution

This is from a web assignment from a ODE course which just started. We have only cover first order linear, homogenous ODE's and vairable seperable. I have no idea where to start here. Am I just overlooking something? Do I need to work backwards from the solutions? Any help to get me started would be greatly appreciated.

 

[Mark44]

Homework Statement

Match each of the differential equations with a solution from the list below.
1. 2x^2 * y'' + 3xy' = y
2. y'' + 12y' + 36y = 0
3. y'' - 12y' + 36y = 0
4. y'' + y = 0

And then the possible solutions A-D

Homework Equations

The Attempt at a Solution

This is from a web assignment from a ODE course which just started. We have only cover first order linear, homogenous ODE's and vairable seperable. I have no idea where to start here. Am I just overlooking something? Do I need to work backwards from the solutions? Any help to get me started would be greatly appreciated.

If you haven't done anything with 2nd order DEs yet, probably the best course of action is find the 1st and 2nd derivatives of the solutions you are given, and substitute them into each of the four given differential equations.