1. The problem statement, all variables and given/known data solve the IVP y''-8y'+16y=0 y(0)=2 y'(0)=7 2. Relevant equations 3. The attempt at a solution auxiliary equation: r2-8r+16=0 (r-4)2=0 so we have r=4 with m=2 y(x)= c1e4x+c2xe4x y(0)--> c1e0 + 0 = 2 c1=2 now we have: y(x)=2e4x+c2xe4x take first derivative y'(x) = 8e4x+c2e4x+4c2xe4x (product rule) y'(0) ----> 8e0+c2e0+ 0 = 7 8+c2=7 c2=-1 so our final equation is: y(x)=2e4x-xe4x Everything seems ok, but just wanted to run it by here to make sure it's all done correctly. thanks all!