Solve differential equationsin(x) dy/dx+(cos(x))y=0, y((7pi)/6)=-2

Lennie Carroll 2020-11-14 Answered

Solve differential equation \(\sin(x) dy/dx+(\cos(x))y=0\), \(y((7\pi)/6)=-2\)

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Expert Answer

Arnold Odonnell
Answered 2020-11-15 Author has 18084 answers

\(\sin x dy/dx+ y\cos x=0\)
\(\sin x dy= -y\cos x dx\)
\(dy/y= - \cos x/\sin x dx\)
\(\int dy/y= -\int \cos x/\sin x dx\)
\(\ln |(y)|= -\ln |(\sin x)|+\ln |(C)|\)
\(\ln y= \ln (C/\sin x)\)
\(y\sin x= C\)
Now, We are applying the given Initial Condition is as follow
\(y((7\pi)/6)= -2\)
\(-2*\sin((7\pi)/6)= C\) \(-2* -1= C\) \(\therefore\sin(7\pi/6)= -1\)
C=2
\(y\sin x= 2\)

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