Differential equations - backwards problem

[dmoney123]

Homework Statement

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

Homework Equations

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.

 

[LCKurtz]

Look at this thread:
https://www.physicsforums.com/threads/solving-a-first-order-initial-value-problem.779622/

 

[Simon Bridge]

Find an expression that has y''(t) in it.
[edit]... of LCKurtz link: that's interesting: someone in your class?

 

[LCKurtz]

Find an expression that has y''(t) in it.
[edit]... of LCKurtz link: that's interesting: someone in your class?

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

 

[Ray Vickson]

Homework Statement

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

Homework Equations

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.

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