Hi,(adsbygoogle = window.adsbygoogle || []).push({});

I've come across a problem in my differential equations book that I can't seem to be able to solve (it's not a homework problem, I'm just practicing):

"Using matrix algebra techniques and the method of undetermined coefficients, find a general solution for

x''(t) + y'(t) - x(t) + y(t) = -1,

x'(t) + y'(t) - x(t) = t^2 "

At first, I tried to change this system to a system of first-order differential functions only using the following substitutions:

x1(t) = x(t)

x2(t) = x'(t)

x3(t) = y(t)

Which leads to the following system in matrix form:

[itex]\left[ \begin{array}{c} x1' \\ x2' \\ x3' \end{array} \right] = \left[ \begin{array}{ccc} 0 & 1 & 0 \\ 0 & 1 & -1 \\ 1 & -1 & 0 \end{array} \right] * \left[ \begin{array}{c} x1 \\ x2 \\ x3 \end{array} \right] + \left[ \begin{array}{c} 0 \\ -t^2 - 1 \\ t^2 \end{array} \right] [/itex]

Next, I solved the system of heterogeneous equations associated with this system, which also wasn't a problem. But now I'm stuck:

The nonhomogeneous part suggests a particular solution of the form [itex]Bt^2+Ct+D[/itex], with B, C, and D being vectors to be determined. Putting everything into the system yields

[itex]2*Bt+C = A*(Bt^2 + Ct + D) + \left[ \begin{array}{c} 0 \\ -t^2-1 \\ t^2 \end{array} \right][/itex], with A being the coefficient matrix of my original system. But how do I proceed from here?

Thanks,

Alex

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Solving system of differential equations using undetermined coefficients

**Physics Forums | Science Articles, Homework Help, Discussion**