Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

For example, ODE: $y'' + y = 0$ solve this problem using MAPLE

f(x) = _C1*sin(x)+_C2*cos(x)

My question is Eigenvalue for $D^2+1=0$ is $\pm i$ so general solution is $f(x) = c_1 e^{ix}+ c_2 e^{-ix}$ according to Euler's formula $$f(x) = c_1(\cos x+i\sin x) + c_2(\cos x-i\sin x )$$ it is different from the general solution generated by MAPLE why?


share|cite|improve this question
up vote 0 down vote accepted

Your solution is the general solution assuming f(x) is complex, and your constants C1 and C2 are also complex. You can rearrange it as f(x) = (C1 + C2) cos(x) + i (C1 - C2) sin(x) or f(x) = A1 cos(x) + A2 sin(x) wherne A1 and A2 are complex constants. If course if you want to restrict f(x) to be a real function, A1 and A2 must be real. That condition is the equivalent to C1 and C2 being complex conjugates, so that C1 + C2 is real and C1 - C2 is imaginary.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.