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
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