# Y" -y' -2y = 4(t^2) , y(0) = 1 , y'(0) =4?

## Homework Statement

the answer that i found id 2(e^t) -1 , why it is wrong ? the answer given is cosht

## The Attempt at a Solution

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SteamKing
Staff Emeritus
Homework Helper
Did you substitute your answer back into the original differential equation? Did it satisfy this equation and all of the initial conditions?

If the answer is no, it didn't, then that's why.

BTW: You should not put one equation in the thread title when the problem covers a completely different equation.

Mark44
Mentor
BTW: You should not put one equation in the thread title when the problem covers a completely different equation.
Furthermore, the equation should be in the problem statement section, not in the thread title.

LCKurtz
Homework Helper
Gold Member

## Homework Statement

the answer that i found id 2(e^t) -1 , why it is wrong ? the answer given is cosht

## The Attempt at a Solution

If you try your answer and the book's answer in the original equation, you will see both are incorrect. Either that, or you copied the problem incorrectly. In your work, $\mathcal L(y) \ne s Y(s)$. Also, there is no reason to post this problem as an image instead of just typing it.

HallsofIvy
Homework Helper
Are you required to use the Laplace transform? This is a simple second order, linear equation with constant coefficients. It has characteristic equation $r^2- r- 2= (r- 2)(r+ 1)$ and a "specific solution" to the entire equation must be of the form $Ax^2+ Bx+ C$.

Mark44
Mentor
Are you required to use the Laplace transform? This is a simple second order, linear equation with constant coefficients. It has characteristic equation $r^2- r- 2= (r- 2)(r+ 1)$ and a "specific solution" to the entire equation must be of the form $Ax^2+ Bx+ C$.
No. The DE in the title is different from the one in the image that the OP posted. The initial value problem in the posted image is y'' - y = 0, y(0) = 1, y'(0) = 1.

HallsofIvy