## Science & engineering math: system of differential equations

1. The problem statement, all variables and given/known data

Solve the system of differential equations:
y'(t) + z(t) = t
y"(t) - z(t) = e-t
Subject to y(0) = 3, y'(0) = -2, and z(0) = 0

2. Relevant equations

My professor did an example in class that was much simpler and solved it using Kramer's rule.

3. The attempt at a solution
I don't know how to start it. I thought about rearranging the equations so that one was equal to y'(t) and the other was equal to z(t), but I'm not sure that would work...

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 Recognitions: Homework Help What about adding the equations so as z(t) cancels? ehild
 I would definitely start off as ehild has suggested.

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## Science & engineering math: system of differential equations

There is, however, a problem with the entire exercise. Doing as ehild suggests gives you a second order differential equation in y only which you can solve and then use the initial conditions to give a specific solution for y. But there is no derivative of z in these equations- once you know y, z is fixed and you have no constant to choose to make z(0)= 0. Was one or both of those "z"s supposed to be z'? If not then any one of the three conditions, y(0)= 3, y'(0)= -2, z(0)=n 0, can be dropped to give a solution but there is not y, z, satisfying the equations and all three of the conditions.

 Oh my gosh yes there was supposed to be a z' in the first equation So it is: y'(t) + z'(t) = t The second equation is correct though, so sorry for any confusion!!

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 Quote by chatterbug219 Oh my gosh yes there was supposed to be a z' in the first equation So it is: y'(t) + z'(t) = t The second equation is correct though, so sorry for any confusion!!
Then you can integrate the first equation and add to the second.

ehild

 Tags differential eqs, system of equations