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posted by  CalcKumakun on 7/24/2008 4:37:33 PM  |  status: Closed  

First-Order DE General Solution Problem

Course Textbook Chapter Problem
Differential Equations Differential Equations and Bounday Value Problem 4th Ed 1.6 50
Question Details:
Can someone help show me the steps in doing this problem to find a general solution of a reducible second-order differential equation
  I substituted y' with p and y'' with p*p' but I'm not sure what to do with the x since solving it gives x^2+xy+y^2 so it can't be separable.
Any help is greatly appreciated. 
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posted by PlayAirGuitar on 7/25/2008 6:12:40 AM  |  status: Live
Asker's Rating: Lifesaver   
CalcKumakun's comment:
"thanks! Helped a lot."
Response Details:
p = x + y'
p' = 1 + y''

y'' = p' - 1
y'' = (x + y')2 = p2

p2 = p' - 1
p' = p2 + 1




arctan p = x + C1
p = tan(x + C1)

p = x + y'

x + y' = tan(x + C1)
y' = tan(x + C1) - x
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