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# What am I doing wrong with this initial value problem? Watch

1. Solve the initial value problem:

dx/dt = (1-t)x with initial value being x(2)=0

dx/x = (1-t)dt

Then integrate both sides:

1/x = t - t^2/2 + c

Applying x(2)=0:

0 = 1/(t - t^2/2 + c)

0 = 1/c

c = ?
2. When you integrate both sides is when the mistake pops up. yet I see no logarithms in your answer.
3. when you integrate both sides you have a log:

LHS:

on the RHS, introduce the constant of integration in log form:

you can exponentiate and then use the IC, or move ln(k) to the LHS, use the IC, solve for k, then exponentiate
4. you could also use the limits of integration thus:

1) move the expression involving t to the LHS and integrate between respective limits:

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Updated: January 28, 2015
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