# Differential equations - backwards problem

OP warned about not including efforts

## 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

## 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
Homework Helper
Gold Member
dmoney123
Simon Bridge
Homework Helper
Find an expression that has y''(t) in it.

LCKurtz
Homework Helper
Gold Member
Find an expression that has y''(t) in it.

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

Ray Vickson
Homework Helper
Dearly Missed

## 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

## 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)##.