Solution of Euler Differential Equation Using Ansatz Method

[dave4000]

Homework Statement

Solve the euler differential equation

\x^{2}y^{''}+3xy'-3y=0
<br /> \int_X f = \lim\int_X f_n &lt; \infty<br />
by making the ansatz y(x)=cx^{m}, where c and m are constants.&lt;br /&gt; &lt;br /&gt; &lt;h2&gt;The Attempt at a Solution&lt;/h2&gt;&lt;br /&gt; &lt;br /&gt; y(x)0=c^{m}&amp;amp;lt;br /&amp;amp;gt; y^{&amp;amp;amp;amp;#039;}(x)=cm^{m-1}&amp;amp;amp;amp;lt;br /&amp;amp;amp;amp;gt; y^{&amp;amp;amp;amp;amp;amp;#039;&amp;amp;amp;amp;amp;amp;#039;}(x)=cm(m-1)^{m-2}&amp;amp;amp;amp;amp;amp;lt;br /&amp;amp;amp;amp;amp;amp;gt; &amp;amp;amp;amp;amp;amp;lt;br /&amp;amp;amp;amp;amp;amp;gt; m(m-1)+3m-3=0&amp;amp;amp;amp;amp;amp;amp;amp;lt;br /&amp;amp;amp;amp;amp;amp;amp;amp;gt; m^2+2m-3=0&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;lt;br /&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;gt; (m-1)(m+3)=0&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;lt;br /&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;gt; m=-3 or m=1&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;lt;br /&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;gt; &amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;lt;br /&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;gt; Is this the solution or can c be found?

 

[dave4000]

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?

 

[Astronuc]

Latex maybe out due to technical problems.

Is one sure of the function before the y' term - 3x^{2}?

 

[dave4000]

*Correction made* :)

 

[dave4000]

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...

 

[dave4000]

so...er...c?

 

[dave4000]

since no innitial conditions were given i shall take irt that c cannot be found.