Given that y=x is a solution of:

(X^2)y"-(2x+5x^2)y'+(2+5x)y=0 in x>0,

Find another solution yc of the same equation such that {x,yc} is a fundamental set of solutions.

yc = ?

What do I do? I wanted to use series solutions, but it's a singular point. So then I decided to try using reduction of order to get y2 = uy1 (where you solve for u' and integrate, etc). However, that turned into an unsolvable integral... so I'm stuck! Please help!

2. The procedure to arrive, once you know a solution $\displaystyle y_{1}$ of this type of equation, to a second solution $\displaystyle y_{2}$ independent from it, is illustrated here...

http://www.mathhelpforum.com/math-help/calculus/82519-variation-parameter-2nd-order-ode.html

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$

3. ## Thanks!

Thank you very much! It appears we have not yet learned this in class (perhaps there is another method of solution), but it allowed me to complete my webworks. I will take note of this method! Thanks again!

4. Originally Posted by outatime1.21
Given that y=x is a solution of:

(X^2)y"-(2x+5x^2)y'+(2+5x)y=0 in x>0,

Find another solution yc of the same equation such that {x,yc} is a fundamental set of solutions.

yc = ?

What do I do? I wanted to use series solutions, but it's a singular point. So then I decided to try using reduction of order to get y2 = uy1 (where you solve for u' and integrate, etc). However, that turned into an unsolvable integral... so I'm stuck! Please help!
It should have worked fine. Why not show us some of your work.