Q: Find the Wronskian of two solutions of the given differential equation without solving the equation
cos(t)y''+sin(t)y'-ty=0
Answer:
y''+sin(t)y'/cos(t)-ty/cos(t)=0
P(t)=sin(t)/cos(t)
W=ce^(∫p(t)dt)
=ce^(-∫(sin(t)/cos(t))dt) let u=cos(t), du=-sin(t)dt
=ce^(∫1/u du)
=ce^(lnu)
=cu
=ccos(t)
