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
5482 Views
See similar Further Mathematics A Level tutorsRelated Further Mathematics A Level answers
All answers ▸Prove by induction that, for all integers n >=1 , ∑(from r=1 to n) r(2r−1)(3r−1)=(n/6)(n+1)(9n^2 -n−2). Assume that 9(k+1)^2 -(k+1)-2=9k^2 +17k+6
Whats the derivative of sin(3x)?
Find the general solution of the second order differential equation y''(t)+y(t) = 5exp(2t)
It is given that z = 3i(7-i)(i+1). Show that z can be written in the form 24i - k. State the integer k.