### Author Topic: WW-2, Problem 7  (Read 529 times)

#### Yudi Chen

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##### WW-2, Problem 7
« on: September 21, 2014, 05:29:31 PM »
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.
« Last Edit: September 21, 2014, 06:19:31 PM by Victor Ivrii »

#### Victor Ivrii

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##### Re: WW-2, Problem 7
« Reply #1 on: September 21, 2014, 06:26:25 PM »
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

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##### Re: WW-2, Problem 7
« Reply #2 on: September 22, 2014, 03:45:45 PM »
but Bernoulli Equations require the form to be $dy/dx + p(x)y = q(x)y^n$ ?
« Last Edit: September 22, 2014, 05:44:42 PM by Victor Ivrii »

#### Victor Ivrii

but Bernoulli Equations require the form to be $dy/dx + p(x)y = q(x)y^n$ ?
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 $z'=\ldots$