Fun Differential Equations Again!

[Frogger888]

Hi guys, I have three problems that I have done for differential equations and I wonder if someone could check my answers to make sure I did them right. Thanks I used Cauch-Euler Method

1. 4x^(2)y''+4xy"-y=0 Ans. y=c1x^-(1/2) + c2x^(1/2)

2. x^(2)y''-5xy'+9y=0 Ans. y=c1x^3 + c2x^(3)ln(x)

3. x^(2)y''-3xy'+13y=0 Ans. y= x^(2) [c1cos(3lnx) + c2sin(3lnx)]

c1=c sub 1
c2=c sub 2

 

[Unco]

They are all correct (provided the first one has a 4xy' term). Euler-Cauchy is relatively straightforward.

 

[Frogger888]

I messed up on the 1st problem and wrote two y'' the second one was supposed to be y'. Thanks for the help again. Much appreciated