18.03 Spring 10 Exercises 1B-2 c)

Find an integrating factor and solve:

(t^2 + 4)dt + tdx = xdt

I put this ODE in form: x - t(dx/dt) = t^2 + 4

The solutions take some steps I am not familiar with. I found integrating factor e^((-2(t^2)) but the solution uses integrating factor 1/t^2 and I cannot see the connection in the algebra.

The solutions are at this URL:

http://ocw.mit.edu/courses/mathematics/18-03-differential-equations-spring-2010/readings/notes_exe/MIT18_03S10_1ex.pdf

Question

18.03 Spring 10 Exercises 1B-2 c)

Find an integrating factor and solve:

(t^2 + 4)dt + tdx = xdt

I put this ODE in form: x - t(dx/dt) = t^2 + 4

The solutions take some steps I am not familiar with. I found integrating factor e^((-2(t^2)) but the solution uses integrating factor 1/t^2 and I cannot see the connection in the algebra.

The solutions are at this URL:

http://ocw.mit.edu/courses/mathematics/18-03-differential-equations-spring-2010/readings/notes_exe/MIT18_03S10_1ex.pdf