Question

Solving the differential equation (2x+y+1)(dy/dx)=1

Answer 1

I've thought about trying to write it as an exact equation, using an integrating factor. Of course it's not seperable. I can't see any way of writing it as a function f(x/y). I'm pretty shaking with this subject, so any help would be appreciated!

Answer 2

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Answer 3

haha. No I'm not.

Answer 4

is it the whole question ?

Answer 5

yes

Answer 6

dy/dx = 1/2x+y+1
let P = 1/2x+y+1 = (2x+y+1)^-1

Answer 7

So substitution for the whole expression on the right?

Answer 8

find the dP/dx

Answer 9

So isn't that the equivalent of taking the second derivative of y with respect to x?

Answer 10

dP/dx in implicite, won't equivalent

Answer 11

So now I have a second order differential equation \[d^2y/dx^2=dP/dx=-(2+ydy/dx)/(2x+y+1)\] ?

Answer 12

Sorry the denominator on the right hand side of the expression should be squared

Answer 13

in dP/dx result, dy/dx change into P and at this step we reach 1st order, and we shouldnt have y variable but in ur case why y cant be move out

Answer 14

for example:
P = 3x + 2y -10
dP/dx = 3+2 dy/dx
F(p)= P = dy/dx
dP/dx = 3 + 2 P
integral (1/ (3+2P ) ) dP = integral (dx)

Answer 15

sorry - how does F(p)=P?

Answer 16

Otherwise...yeah I see what's going on. Its a good trick. But I guess I have to find a different substitution to solve this equation?

Answer 17

sorry because im not english native, so hard for me to explain

Answer 18

hey, that's ok. I really do appreciate that you're trying!

Answer 19

check this out http://www.wolframalpha.com/input/?i=%282x%2By%2B1%29%28dy%2Fdx%29%3D1