Originally Posted by

**BKennedy** I was wondering if someone could help me with where I am going wrong on this question. I will post the work I have completed, which gave me the wrong solution.

The Question is:

du/dt= e^(1t-3.2u) u(0)=2.6

Find the function u(t) from the differential equation and the initial conditions...

u(t)=__________

This is what I have done:

**du/dt = e^t/e^(-3.2u)**

e^(-3.2u) du = e^t dt

integrate both sides

-1/3.2 e^(-3.2u) = e^t + c, where c is constant

e^(-3.2u) = -3.2 e^t + c

-3.2 u = ln(-3.2 e^t +c)

u = -1/3.2 ln(-3.2 e^t + c)

Solving for c by using the initial condition

u(0) = -1/3.2 ln(-3.2 + c) = 2.6

Solve for c:

ln(-3.2+c) = -8.32

c = e^-8.32 + 3.2

c = 3.2002

u(t) = -1/3.2 ln (-3.2 e^t + 3.2002)

But this is not correct