Problem 86 Solution

Let f(t)=account value at time t.

f'(t)=t*f(t).

Let y=f(t).

dy/dt=ty.

dy=ty dt.

dy/y = t dt.

Integrating both sides:

ln(y) = t²/2 + C.

y = exp(t²/2 + C).

y = exp(t²/2). Since y=1 when t=0

Michael Shackleford, A.S.A.