MAT244--2019F > Quiz-3

TUT0801 quiz3

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XueQiWang:
Q：Find the Wronskian of two solutions of the given differential equation without solving the equation.
x^2·y''+xy'+(x^2-v^2)y=0

A: x^2·y''+xy'+(x^2-v^2)y=0
both side divided by x^2:  y''+y'/x+(x^2-v^2)y/x^2=0
such that: p(x)=1/x
W=ce^(-∫p(x)dx)=ce^(-∫(1/x)dx)=ce^(-ln(x)+c)=ce^(ln(1/x)+c)=cx^-1·e^c
therefore: W=c/x