Integrate dx/(1-x): Solve (2/3a)(1-(1-aW)^(3/2))

  • Thread starter Thread starter cycling4life
  • Start date Start date
  • Tags Tags
    Integration
cycling4life
Messages
7
Reaction score
0
In part of a derivation they have, Integrate dx/(1-x) = (1-aW)^(1/2) dW

I get -ln(1-x) = (-2/3a)*(1-aW)^(3/2) but they say it's ln(1/(1-X)) = (2/3a)((1-(1-AW)^(3/2))

Can anyone tell me how they get that extra "1-"?
 
Last edited:
Physics news on Phys.org
-ln(1-x) = (-2/3a)*(1-aW)^(3/2) + Contant
 
Thread 'Direction Fields and Isoclines'
I sketched the isoclines for $$ m=-1,0,1,2 $$. Since both $$ \frac{dy}{dx} $$ and $$ D_{y} \frac{dy}{dx} $$ are continuous on the square region R defined by $$ -4\leq x \leq 4, -4 \leq y \leq 4 $$ the existence and uniqueness theorem guarantees that if we pick a point in the interior that lies on an isocline there will be a unique differentiable function (solution) passing through that point. I understand that a solution exists but I unsure how to actually sketch it. For example, consider a...
Back
Top