Rearranging an equation involving an integral

[knockout_artist]

Homework Statement

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 [/B]

 

[PeroK]

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 $a$?!

 

[fresh_42]

You lost a term. You can almost read the squared equation without any calculations. Then solve for $(y(x)')^2$ and take the root.