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Obtain the solution that satisfies the given conditions of the differential equation, dy/dx = tanxtany , y = pi/4 at x = pi/4

Guest May 28, 2015

Best Answer 

 #1
avatar+26716 
+15

Differential eqn.

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Alan  May 28, 2015
 #1
avatar+26716 
+15
Best Answer

Differential eqn.

.

Alan  May 28, 2015
 #2
avatar+92623 
+5

I am looking at this a bit at a time Alan.

 

$$\\\int{\frac{dy}{tan(y)}}\\\\
=\int{\frac{cos(y)}{sin(y)}}dy\\\\
=ln(sin(y))+k$$

 

Isn't that correct ?

Melody  Jun 3, 2015
 #3
avatar+26716 
+5

Same thing Melody:

 

 comparison

 

I might have got to the end result quicker if I'd used your formulation though!

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Alan  Jun 3, 2015
 #4
avatar+92623 
0

Thank Alan 

Melody  Jun 4, 2015
 #5
avatar+889 
+5

Also Melody, it's often advantageous to write the constant of integration as

$$\ln(k).$$

That allows the result to be written as

$$\ln(\sin y) + \ln(k) = \ln(k \sin y)$$

making later simplification easier.

Bertie  Jun 4, 2015
 #6
avatar+92623 
0

Thanks Bertie   

That makes god sense  :)

Melody  Jun 4, 2015

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