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Reduction of order ODE

  • Thread starter manenbu
  • Start date
  • #1
103
0

Homework Statement



Solve:
[tex]
y'' -y' e^{y'^2-y^2} = 0
[/tex]

y(0) = 1
y'(0) = 0

Homework Equations





The Attempt at a Solution



No idea how to use it.
If I use the substituion y' = p, and y'' = p'p I need to integrate [itex]e^{y^2}[/itex] which is unintegratable. What should I do?
 

Answers and Replies

  • #2
gabbagabbahey
Homework Helper
Gold Member
5,002
6
According to your DE and initial conditions, what is [itex]y''(0)[/itex]? How about [tex]\left.\frac{d^n y}{dx^n}\right|_{x=0}[/tex] ? What might you expect the solution to be if all the derivatives are zero at some point? Can you prove that is the only solution?
 
  • #3
103
0
I get what you're trying to say - that the solution is y=1.
I don't know how to prove it though.
 

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