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Rearranging an equation involving an integral

  • #1

Homework Statement


rearrange.png

Homework Equations



How do we get y(x) ?
should y'(x) in the sqrt not cancel the y/(x) on the RHS ?
Does y(x) comes back because of integrating 1 with dy ?


The Attempt at a Solution



w(x)y'(x) = A (1 +y'(x)2)1/2

(w(x)y'(x) )2 = ( A (1 +y'(x)2)1/2 )2

w(x)2y'(x)2 = A2 + A2 )

y'(x)2 = {A2 1 + A2 y'(x)2) } /w(x)2

1 = {A2 + A2 } /w(x)2
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Answers and Replies

  • #2
PeroK
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Why do you think you can cancel ##y'(x)## like that?

Effectively you have gone from ##a = 1+ab## to ##1 = 1+b##, by dividing both sides by ##a##?!
 
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  • #3
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You lost a term. You can almost read the squared equation without any calculations. Then solve for ##(y(x)')^2## and take the root.
 
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