(x+y)dy/dx = x^2+xy+x+1 ; y=v-x

So i did the substitution and ended up with vdv/dx - v =xv+x+1

and, if correct, i've no idea how to solve.

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- March 21st 2009, 09:44 AMErghhhSolving differential equations using a change of variable
(x+y)dy/dx = x^2+xy+x+1 ; y=v-x

So i did the substitution and ended up with vdv/dx - v =xv+x+1

and, if correct, i've no idea how to solve. - March 21st 2009, 09:51 AMADARSH
- March 21st 2009, 10:25 AMErghhh
So then i got (y+x)ln|x+y+1|=(1/2)(x^2) +x+c

The answer, according to my book, is y=ln|x+y+1| +(1/2)(x^2)+C

I'm unsure of how to get there.. - March 21st 2009, 10:45 AMrunning-gag
Hi

A sign - is missing

(y+x)-ln|x+y+1|=(1/2)(x^2) +x+c

Then y=ln|x+y+1| +(1/2)(x^2)+c - March 21st 2009, 10:46 AMErghhh
Can you explain where that minus sign has come from?

- March 21st 2009, 10:50 AMrunning-gag
- March 21st 2009, 10:51 AMHallsofIvy

Intgrate that.

running-gag got in ahead of me!