Thread: Find the second solution of a differential equation

Need help...Given a differential equation and its first solution y1 find the second solution y2 using reduction of order.

x^2 y'' - 3xy' +5y =0; y1 = x^2 cos (ln x)

thank you so much!

Originally Posted by kithy

Need help...Given a differential equation and its first solution y1 find the second solution y2 using reduction of order.

x^2 y'' - 3xy' +5y =0; y1 = x^2 cos (ln x)

thank you so much!

Let

Then






Now look at the term proportional to v(x):


But this is just 0 according to the differential equation. So we get


and you can take it from here.

-Dan