1. ## Solve dy/dx=-1-x+xy(x)+y^2 (x)

pls help solve
dy/dx=-1-x+xy(x)+y^2 (x)

2. Originally Posted by snehalkhair
pls help solve
dy/dx=-1-x+xy(x)+y^2 (x)
This is a Ricatti equation. I suggest you review the appropriate theory.

3. I will say that one solution to this ODE is $y = 1$.

4. Originally Posted by Danny
I will say that one solution to this ODE is $y = 1$.
Is that because upon substitution dy/dx =0 implies y must be a constant? But how 1?

5. Originally Posted by bugatti79
Is that because upon substitution dy/dx =0 implies y must be a constant? But how 1?
$y = 1$ satisfies the original ODE. Just plug it in and see for yourself. I believe Danny mentioned this because if you have a particular solution for a Ricatti equation, you can get the general equation by using the appropriate method, as mr f suggested the OP'er look up.

6. Originally Posted by Ackbeet
$y = 1$ satisfies the original ODE. Just plug it in and see for yourself. I believe Danny mentioned this because if you have a particular solution for a Ricatti equation, you can get the general equation by using the appropriate method, as mr f suggested the OP'er look up.
Thats what I did..i think. just subbing in 1 for y in the rhs of ODE we get dy/dx=0.

7. Originally Posted by bugatti79
Thats what I did..i think. just subbing in 1 for y in the rhs of ODE we get dy/dx=0.
Yes, that's the point. Since y= 1 (for all x) is a constant its derivative is 0. 1 is the only value that also makes the right hand side 0.