Identifying the type/form for a Differential Equation

[Canaldigger]

Homework Statement

For the following Differential Equation, identify the type(separable, linear, exact, homogeneous, Bernoulli), then obtain a general solution with DERIVE

(2x+y+1)y'=1

Homework Equations

The Attempt at a Solution

I'm fairly certain that this is not a homogeneous or exact, but I cannot figure out which other form it could fit with.

I thought possibly linear, but only ended up with y' - 1/(2x+y+1)=0. I don't think p(x) can contain y so that would not fit the linear form. I think I need to rearrange some terms but I'm not entirely sure.

 

[Canaldigger]

Right, not homogeneous and not exact. Your equation contains a yy' term. That makes in nonlinear. What else is there in your list?

The assignment is to learn how to use the Derive program properly, so I could easily use the "any first order DE" command to obtain a general solution, but that defeats the whole purpose.

At the moment I only know how to solve for separable, linear, exact, homogeneous, and bernoulli.

 

[Dick]

The assignment is to learn how to use the Derive program properly, so I could easily use the "any first order DE" command to obtain a general solution, but that defeats the whole purpose.

At the moment I only know how to solve for separable, linear, exact, homogeneous, and bernoulli.

It looks to me like it's none of those. But I think it would become separable after a change of variable.

 

[Canaldigger]

It looks to me like it's none of those. But I think it would become separable after a change of variable.

Yeah, I just noticed that the first part is in Ax+By+c form so I think reduction to seperable variables will work.

I pretty sure I can solve it now, but the problem seems pointless for computer input, since I could solve it faster by hand.