Question
Asked Jul 22, 2019

Solve the first order differential equation using any acceptable method.

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

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Expert Answer

Step 1

We have given First Order Differential Equation,

dy
+y cosx = 0
dx
Sinx
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dy +y cosx = 0 dx Sinx

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Step 2

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
dy
COSX
dx
sinx
у
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sinx dy -ycosx dx dy COSX dx sinx у

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Step 3

Now, Integrating both sides o...

- S
cosx
f dy
dx
sinx
ny nsinx| n|C
C
ny In
sinx)
ysinx C
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- S cosx f dy dx sinx ny nsinx| n|C C ny In sinx) ysinx C

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