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Homework Statement
the answer that i found id 2(e^t) -1 , why it is wrong ? the answer given is cosht
Furthermore, the equation should be in the problem statement section, not in the thread title.BTW: You should not put one equation in the thread title when the problem covers a completely different equation.
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.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
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.Are you required to use the Laplace transform? This is a simple second order, linear equation with constant coefficients. It has characteristic equation [itex]r^2- r- 2= (r- 2)(r+ 1)[/itex] and a "specific solution" to the entire equation must be of the form [itex]Ax^2+ Bx+ C[/itex].