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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

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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

#1
+26399
+15

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Alan  May 28, 2015
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#1
+26399
+15

.

Alan  May 28, 2015
#2
+91435
+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
+26399
+5

Same thing Melody:

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

.

Alan  Jun 3, 2015
#4
+91435
0

Thank Alan

Melody  Jun 4, 2015
#5
+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
+91435
0

Thanks Bertie

That makes god sense  :)

Melody  Jun 4, 2015

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