# Differential equations - backwards problem

Tags:
1. Nov 2, 2014

### dmoney123

• OP warned about not including efforts
1. The problem statement, all variables and given/known data
If y=y(t) is the solution of the initial value problem

{
y'+(2t+1)y=2cos(t)

y(0)=2

then

y''(0)=?

it is a multiple choice practice problem with choices

y''(0)=2
y''(0)=-2
y''(0)=4
y''(0)=0
y''(0)=-4

2. Relevant equations

3. The attempt at a solution

Im really not sure how to go about solving this.

When I try to solve for y(t) i get a huge mess.

2. Nov 2, 2014

3. Nov 2, 2014

### Simon Bridge

Find an expression that has y''(t) in it.

4. Nov 2, 2014

### LCKurtz

?? Who are you addressing? Me? Not one of my classes. I retired over 10 years ago.

5. Nov 3, 2014

### Ray Vickson

Why solve at all? You have $y'(t) = 2 \cos(t) - (2t +1) y(t)$, so you can get $y''(t)$.