Solve the first order differential equation using any acceptable method. sin(x)

tebollahb 2022-01-20 Answered
Solve the first order differential equation using any acceptable method.
sin(x)dydx+(cos(x))y=0, y(7π6)=2
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Expert Answer

otoplilp1
Answered 2022-01-20 Author has 41 answers
We have given First Order Differential Equation,
sin(x)dydx+y (cos(x))=0
Now, We are using Variable Separable Method for solving the First Order Linear Differential Equation is as follows:
First, we need to separate the variable with the respective derivatives:
sinx dy=ycosx dx
dyy=cosxsinxdx
Now, Integrating both sides of the above equation:
dyy=cosxsinxdx
ln|y|=ln|sinx|+ln|C|
lny=ln(Csinx)
ysinx=C
Now, We are applying the given Initial Condition is as follow:
y(7π6)=2
2×sin(7π6)=C
2×1=C      sin(7π6)=1
C=2
Answer:
The resulting curve of the First Order Linear Differential Equation is y sinx =2.

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Barbara Meeker
Answered 2022-01-21 Author has 38 answers
sinxdydx+(cosx)y=0
y(7x6)=2
dydx+(cosx)y=0
dydx=(cosx)y
dyy=cosx dx
lny=ln(sinx)+lnC
lny+lnsinx=lnC
y(sinx)=C
y(7x6)=2
2sin(7x6)=C
2(12)=C    C=1
(sinx)y=1
y=cosec x

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