Question

Solve the given differential equation by using an appropriate substitution. The DE is of the form dy dx = f(Ax + By + C), which is given in (5) of Section 2.5. dy/dx = (x + y + 1)^2

Answer 1

any help will be much appreciated

Answer 2

I tried that and then integrated both sides but it says I was wrong

Answer 3

du/dx = 1 + dy/dx

Answer 4

\(\color{blue}{\text{Originally Posted by}}\) @SithsAndGiggles
Substitution is the first thing that comes to mind, but not sure how it'll work out:
\[u=x+y+1~~\Rightarrow~~\frac{du}{dx}=\frac{dy}{dx}\color{red}{+1}\]
\[\frac{dy}{dx}=(x+y+1)^2~~\iff~~\frac{du}{dx}\color{red}{-1}=u^2\]
So yeah it does, now you have a simple separable equation.
\(\color{blue}{\text{End of Quote}}\)

Thanks to @eashy for catching an error!

Answer 5

Im still not getting it, but thanks guys

Answer 6

Are you getting this?\[\frac{du}{dx}=u^2+1\\
\int\frac{du}{u^2+1}=\int dx\]

Answer 7

yea so x=tan^(-1)(x+y+1)

Answer 8

+C

Answer 9

Do you have an answer available, like a multiple choice or one found in the back of your textbook, or do you think it has something to do with how you wrote it? Because it could be that you haven't written the solution explicitly as \(y\) in terms of \(x\).

Answer 10

No and I don't think it mattered if it were explicit or not. Ill ask my prof but this problem is kicking my retrice

Answer 11

I just reallized i forgot to type in the +C when I submitted........