here is the problem i've been working on for acouple days and can't get right...
Given a solution y1=x of the DE x^2y"-xy'+y=0
Find solution by using the reduction of order method
I've worked through it using the substitution y=xu then found the first and second derivative of y and plugged them back into the orig. equation..and for the orig equation i divided everything through buy the leading coeff x^2 to modify the equation to y"-1/xy'+1/x^2y
when i plugged everything into that equation and simplified I got u"+u'+2u
I then let v=u' to get it to a first order equation
which gave me
v'+v+2u and this is where i'm stuck I don't know what to do since there is still a u in the equation