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Need help with differential equation. 
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#1
May2112, 03:56 PM

P: 3

Hello everyone, this is my first post in "Physics Forums"...
I need help with this problem: Verify that y = (x^2/2) + ((x/2)*√(x^2 + 1)) + ln(√(x+√(x^2 +1))) is a solution of the equation 2y = x*y' + ln(y').....(1) I differentiated (y) with respect to (x), and substituted (y' and y) in equation (1), but that led me to nowhere. *The problem might be easy, but I study by myself and have no one to consult, I appreciate any tips or hints, thanks in advance. 


#2
May2112, 06:04 PM

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P: 26,148

Hello Ammar Kurd! Welcome to PF!
(try using the X^{2} button just above the Reply box ) 


#3
May2212, 05:06 AM

P: 3

Thank you for the replay, I got
y' = x + 0.5√(x^{2}+1) + (x^{2} / (2√(x^{2}+1))) + (x+√(x^{2}+1) / (x√(x^{2}+1)+x^{2}+1)) I also tried to simplify the (y) in this way: y = 0.5x^{2} + 0.5x√(x^{2}+1) + ln(√(x+√(x^{2}+1))) = .5x(x+√(x^{2}+1)) + 0.5ln(x+√(x^{2}+1)) then putting G(x) = x+√(x^{2}+1) y becomes: y = 0.5x*G(x) + 0.5ln(G(x)), and y' = 0.5*G(x) +0.5xG'(x) + 0.5*(G'(x)/G(x)) But when I substitute in the differential equation it only get complicated... *Thank you for the x^{2} tip . 


#4
May2212, 06:08 AM

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P: 26,148

Need help with differential equation.
Hello Ammar Kurd!
I don't know how you got that last term, but it simplifies, to 1/√(x^{2}+1) 


#5
May2212, 10:09 AM

P: 3

Thank you, Problem solved 


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