Can someone help with an idea of how to solve the following differential equation and the results obtained:

Thanks for any help!

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- October 26th 2012, 10:11 AMKramerHelp With Differential Equation
Can someone help with an idea of how to solve the following differential equation and the results obtained:

Thanks for any help! - October 26th 2012, 10:51 AMHallsofIvyRe: Help With Differential Equation
My first thought would be to go ahead and do the derivative on the left side: so that . That's an "Euler type" equation- also called and "equi-potential" equation. The change of variable t= ln(x) will convert it to a linear equation with constant coefficients.

A "short cut" that will work here is to try , , and . Putting those into the equation . In order that this be true for all x, we must have . That quadratic equation has roots . The general solution would be for constants A and B. - October 26th 2012, 11:00 AMKramerRe: Help With Differential Equation
Thanks a lot for reply. What would the result be if you tried taking integral on both sides? Would that not help the cause at all?