2nd Order ODE y''+y=0 I come up with the solutions of y1=c1eix, y2=c2e-ix. Now, using these I try to find the cooresponding real-valued solutions: eix=cos(x)+isin(x) e-ix=cos(x)-isin(x) Both of which have real-valued solutions cos(x). However, when I looked this up online, Wikipedia stated that the answer was y=c1sin(x)+c2cos(x). Am I doing something wrong here? Thanks.