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Euler Differential Equation

  • Thread starter dave4000
  • Start date
  • #1
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Homework Statement


Solve the euler differential equation

[tex]\x^{2}y^{''}+3xy'-3y=0[/tex]
[tex]
\int_X f = \lim\int_X f_n < \infty
[/tex]
by making the ansatz [tex]y(x)=cx^{m}[tex], where c and m are constants.

The Attempt at a Solution



[tex]y(x)0=c^{m}[tex]
[tex]y^{'}(x)=cm^{m-1}[tex]
[tex]y^{''}(x)=cm(m-1)^{m-2}[tex]

[tex]m(m-1)+3m-3=0[tex]
[tex]m^2+2m-3=0[tex]
[tex](m-1)(m+3)=0[tex]
[tex]m=-3 or m=1[tex]

Is this the solution or can c be found?
 
Last edited:

Answers and Replies

  • #2
16
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Latex isn't working on this post so here it is without Latex:

Homework Statement


Solve the euler differential equation

x^{2}y''+3xy'-3y=0

by making the ansatz y(x)=cx^{m}, where c and m are constants.

The Attempt at a Solution



y(x)=cx^{m}
y'(x)=cmx^{m-1}
y''(x)=cm(m-1)x^{m-2}

m(m-1)+3m-3=0
m^2+2m-3=0
(m-1)(m+3)=0
m=3 or m=-1

Is this the solution or can c be found?
 
Last edited:
  • #3
Astronuc
Staff Emeritus
Science Advisor
18,704
1,718
Latex maybe out due to technical problems.

Is one sure of the function before the y' term - 3x^{2}?
 
  • #4
16
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*Correction made* :)
 
  • #5
16
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Latex maybe out due to technical problems.

Is one sure of the function before the y' term - 3x^{2}?
This was merely a typo, the orignal problem still remains...
 
  • #6
16
0
so....er...c?
 
  • #7
16
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since no innitial conditions were given i shall take irt that c cannot be found.
 

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