IVP -variation of parameters
ok so here is my *big* problem im stuck on..=[
thank you for your time reading this
dx/dt + x/t - 1 = t^2 ; x(1) = 1
using variation of paramter i did all this:
dx/dt + x/t = t^2 + 1
dx/dt+ x/t = 0 [solve homogeneous equation first]
integrating by parts i get. ..
-lnx = -lnt + c
x = e^(lnt+c) = At
then i find x(t), x'(t)...
x(t) = At, x'(t) = A
now what i did is put these into the ode which was dx/dt + x/t - 1 = t^2
and i get..
A + At/t = t^2 + 1
2A = t^2 + 1
A = (t^2 + 1)/2
and put A into x(t)...
x = ((t^2+1)/2)*t
and x(1) = 1.... now im stuck!
please could anyone guide me through or tell me what i did wrong? =[ am having a nightmare with these