- #1
foo9008
- 678
- 4
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.SteamKing said:BTW: You should not put one equation in the thread title when the problem covers a completely different equation.
foo9008 said: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.HallsofIvy said: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].
The equation for "Y" is -y' -2y = 4(t^2).
The initial conditions for "Y" are y(0) = 1 and y'(0) = 4.
To solve this differential equation, you can use the method of variation of parameters or the method of undetermined coefficients.
To find the particular solution for the given initial conditions, you can substitute the values of y(0) and y'(0) into the general solution of the differential equation and solve for the constants.
This type of differential equation can be used in physics to model the motion of a damped harmonic oscillator, where the acceleration of the object is proportional to its displacement and velocity. It can also be used in engineering to analyze electrical circuits or in biology to study population growth and decay.