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

[foo9008]

Homework Statement

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

Homework Equations

The Attempt at a Solution

 

[SteamKing]

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]

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 Statement

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

Homework Equations

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]

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]

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]

Which is even easier without using the Laplace transform! The characteristic equation is r^2- 1= (r- 1)(r+ 1)= 0.