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

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

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

Answers (1)

2020-11-15
\(sinx dy/dx+ ycosx=0\)
\(sinx dy= -ycosx dx\)
\(dy/y= - cosx/sinx dx\)
\(int dy/y= -int cosx/sinx dx\)
\(ln abs(y)= -ln abs(sinx)+ln abs(C)\)
\(lny= ln (C/sinx)\)
\(ysinx= C\)
Now, We are applying the given Initial Condition is as follow
\(y((7pi)/6)= -2\)
\(-2*sin((7pi)/6)= C\) \(-2* -1= C\) \(:.sin(7pi/6)= -1\)
C=2
\(ysinx= 2\)
0

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