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Solving a Differential Equation 
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#1
Feb611, 05:21 PM

P: 86

1. The problem statement, all variables and given/known data
Solve: 2 * √(x) * (dy/dx) = cos^2(y) y(4) = π/4 2. Relevant equations TRIGONOMETRIC RECIPROCAL IDENTITY: sec(u) = 1 / cos(u) arctan( 1 ) = π / 4 3. The attempt at a solution This is a separable differential equation. 2 * √(x) * (dy/dx) = cos^2(y) 2 * √(x) * dy = cos^2(y) * dx [2 / cos^2(y)] * dy = [1 / √(x)] * dx TRIGONOMETRIC RECIPROCAL IDENTITY: sec(u) = 1 / cos(u) [2 * sec^2(y)] * dy = x^(1/2) * dx ∫ [2 * sec^2(y)] * dy = ∫ x^(1/2) * dx 2 * tan(y) = 2 * √(x) + C y(x) = arctan( √(x) + C) <<< General Solution NOTE: arctan( 1 ) = π / 4 y(4) = arctan( √(4) + C ) y(4) = arctan( 2 + C) C = 1 y(x) = arctan( √(x)  1 ) <<< Particular Solution Is that all correct? Thank you! 


#2
Feb611, 05:26 PM

Sci Advisor
HW Helper
P: 11,896

Looks ok to me.



#3
Feb611, 05:36 PM

P: 86

Thanks! I just remembered that I can check these in my calculator as well.... >.<



#4
Feb611, 07:19 PM

P: 8

Solving a Differential Equation
derivative y=√x+√x
y'=? 


#5
Feb611, 07:27 PM

P: 86

Well, if y=√(x)+√(x) then y=2√(x) and y'=4x^(3/2)/3 but you need to separate the variables first, then integrate not derive, so I don't see how that's relevant...? 


#6
Feb711, 03:10 AM

P: 8




#8
Feb711, 03:15 AM

P: 8




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