1. The problem statement, all variables and given/known data y^(4)+y=0 2. Relevant equations Need to use de Moivre's formula to obtain answer. 3. The attempt at a solution. I can obtain the characteristic equation r^4=-1. From there I tried saying y_1 = cosx and y_2=sinx. However, my book has the answer listed as y= [e^(√(2)x/2)(cos(√(2)/2)x+sin(√(2)/2)x)]+[e^-(√(2)x/2)(cos(√(2)/2)x+sin(√(2)/2)x)]. I am unsure how they obtained this answer. When I asked my teacher he said I had to use the de Moivre formula, but I am unsure how to apply this. PLEASE HELP!