Using the substitution u = ln(x), find the general solution of the differential equation y = x^2*(d^2(y)/dx^2) + x(dy/dx) + y = 0

dy/dx = (dy/du)(1/x), d^2(y)/dx^2 = (d^2(y)/du^2)(1/(x^2)) - (dy/du)*(1/(x^2))   

(x^2)( (d^2(y)/du^2)(1/(x^2)) - (dy/du)(1/(x^2)) ) + x(dy/du)*(1/x) + y = 0       

d^2(y)/du^2 - dy/du + dy/du + y = 0  

d^2(y)/du^2 + y = 0

y = Asin(u) + Bcos(u)

y = Asin(ln(x)) + Bcos(ln(x))                   

IK
Answered by Isis K. Further Mathematics tutor

4043 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

How to use the integrating factor?


Prove by induction that the sum from r=1 to n of (2r-1) is equal to n^2.


If the complex number z = 5 + 4i, work out 1/z.


For what values of x is Cosh^2(x) - Sinh(x) = 5 Give your answer in the form of a logarithm


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences