- #1
Telemachus
- 835
- 30
Homework Statement
Hi. I have this problem, which says: The equation [tex]x^2y''+pxy'+qy=0[/tex] (p and q constants) is called Euler equation. Demonstrate that the change of variable [tex]u=\ln (x)[/tex] transforms the equation to one at constant coefficients.
I haven't done much. I just normalized the equation: [tex]y''+\displaystyle\frac{p}{x}y'+\displaystyle\frac{q}{x^2}y=0[/tex]
Then [tex]P(x)=\displaystyle\frac{p}{x}[/tex] and [tex]Q(x)=\displaystyle\frac{q}{x^2}[/tex]
What should I do now? I thought instead of doing [tex] x= e^u[/tex],
then [tex]y''+ \displaystyle\frac{p}{e^u}y' + \displaystyle\frac{q}{e^{2u}} y=0[/tex] may be this is the right way, cause it seems more like following the problem suggestion.
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