a) Find a function y=f(x) that satisfies the differential equation dy/dx = fifth derivative.

Question

This is one of the questions in my practice test, I tried the basic equation of the trig function such as f(x)= sin(x) or f(x)=-sin(x) however in the fourth derivative they reach the same f(x) and the answer at the book says it is these and the cosine functions which will give the fifth derivative equal to the original equation. What is wrong with my working out?

Answer 1

y = sinx

y ' = cosx or dy/dx = cosx
y '' = -sinx
y ''' = -cosx
y '''' = sinx
y ''''' = cosx

so for y = sinx
the first derivative or dy/dx = cosx
and the fifth derivataive = cosx

so f(x) = sinx