This is actually a problem in algebra as shall be seen. I need to find the general solution for the following differential equation:


The characteristic equation for this is:


Factoring out gives us:


This generates a set of double complex conjugate roots $\lambda_{1,2}=\pm i2$ and $\lambda_{3,4}=\pm i2$

The general solution I get is:


Is this correct? If not please explain in detail where I went wrong. Thank you so much.

  • $\begingroup$ Generally, we write $2i$ rather than $i2$. $\endgroup$ Jan 17, 2015 at 4:18
  • 2
    $\begingroup$ If you want to check your answer, you could always plug each of the four basis solutions into the equation. $\endgroup$
    – hasnohat
    Jan 17, 2015 at 4:23

1 Answer 1


This solution is correct. Good job!

  • $\begingroup$ Thank you. It's all I needed to know. :) $\endgroup$ Jan 17, 2015 at 5:59

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