2018_Question1_b

2018_Question1_b

Substituting in y'=ke^{kx} and y''=k^2e^{kx}, we get that (k^2+k)(k-1)e^{kx}=ke^{2kx}, and so (assuming that k\neq0) we have k^2-1=e^{kx}. But since the left-hand side is a constant, so too must the right-hand side be constant. But this cannot happen, since we assumed that k\neq0. So there are no non-zero values of k that work. If k=0 then the equation is indeed satisfied, so the answer is (b).

1 Like

Excellent!!! :star: :star: :star: :star: :star: :star: