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A tricky 2nd ODE nonhomo delta=0 help needed

  • Thread starter whatababy
  • Start date
  • #1
5
0

Homework Statement


solve the initial value problem:
y''+8.4y'+17.64y=e-4.2x
y(0)=1, y'(0)=1

y(x)=?


Homework Equations


y=yc+yp


The Attempt at a Solution



The way I tried to achieve is to solve the corresponding homo equation first:
y''+8.4y'+17.64y=0, which gives yc;
yc=c1e-4.2x+c2e-4.2xx

Then try to find yp, generally I would assume a yp=Ae-4.2x, but from the yc got above, clearly yp=Ae-4.2x or yp=Ae-4.2xx is not good. If I add one more 'x' in yp assumption,in which it seems A has to be 0, which is not right either....

Any idea? Or I made some mistake?

Meric.
 

Answers and Replies

  • #2
33,162
4,846
Assuming that the work you show is correct, yp = Ax2e-4.2x is the right choice. Plug it into your DE and solve for A.
 

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