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MAT244--2019F => MAT244--Test & Quizzes => Quiz-3 => Topic started by: Jingwen Deng on October 11, 2019, 01:19:54 PM

Title: TUT0602 Quiz 3
Post by: Jingwen Deng on October 11, 2019, 01:19:54 PM
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)