Hi. I have this problem, which says: The equation (p and q constants) is called Euler equation. Demonstrate that the change of variable transforms the equation to one at constant coefficients.
I haven't done much. I just normalized the equation:
Then and
What should I do now? I thought instead of doing , then may be this is the right way, cause it seems more like following the problem suggestion.
Close:
So
and
Just to be clear the expressions on the LHS, y' and y'', are in terms of x ie y'(x) and y''(x) whereas the RHS is describing the derivatives in terms of u.
Now change x into in the differential equation and plug in your new expessions for y' and y''. What does the new equation look like?
-Dan