Third order Euler Differential Equation

[Design]

Homework Statement

x^3y'''-3x^2y''+7xy'-8y=x+e^2x

Edit : Got it thanks

 

[hunt_mat]

Have you thought about trying the solution y=x^{n}? This might lead to an easier cubic to solve.

 

[Design]

Have you thought about trying the solution y=x^{n}? This might lead to an easier cubic to solve.

Not sure how that would work out, only told to use t=lnx. But using y=x^{n} won't cancel the coefficients to be constants.

Edit: I looked up your response on Wikipedia and found something similar on it, never learned to do it this way tho. I'll give it a shot.

 

[hunt_mat]

They will add up to give x^{n} though. for example if y=x^n, then x^{3}y'''(x)=n(n-1)(n-2)x^n, likewise for x^2 and so on. I calculate that the cubic you arrive at the cubic:
<br /> n^{3}-6n^{2}+12n-8<br />
One of the solutions look to be n=2.

Mat

 

[Design]

They will add up to give x^{n} though. for example if y=x^n, then x^{3}y'''(x)=n(n-1)(n-2)x^n, likewise for x^2 and so on. I calculate that the cubic you arrive at the cubic:
<br /> n^{3}-6n^{2}+12n-8<br />
One of the solutions look to be n=2.

Mat

Got it thanks.