MAT244-2014F > MAT244 Math--Lectures

WW-2, Problem 7

(1/1)

Yudi Chen:
I get  $y'=y^2+ (2x-4)y + 4-4x+ x^2$, this looks like the form of Riccati Equations but I have no idea how to solve this.

Victor Ivrii:
Hint: WebWork give you a hint ; it says "Library/FortLewis/DiffEq/1-First-order/05-Substitution-Bernoulli/Lebl-1-5-05.pg"; the same is true for all problems.
Not sure if you (students) can see this [please check]; also not sure if this is a bug or a feature.

Hint: note how I modified your post to employ MathJax

Yudi Chen:
but Bernoulli Equations require the form to be $dy/dx + p(x)y = q(x)y^n$ ?

Victor Ivrii:

--- Quote from: Yudi Chen on September 22, 2014, 03:45:45 PM ---but Bernoulli Equations require the form to be $dy/dx + p(x)y = q(x)y^n$ ?

--- End quote ---

Yes, indeed. But you are missing another key word--"Substitution". Take original equation $y' = (x+y-2)^2$ and plug $z:=x+y-2$; you'll get $z'=\ldots$