# Sample ODE question

• Jul 6th 2010, 06:26 PM
math2009
Sample ODE question
How do solve $\displaystyle\frac{dy}{dx}+y^2+2x=0$ ?
• Jul 6th 2010, 07:52 PM
mr fantastic
Quote:

Originally Posted by math2009
How do solve $\displaystyle\frac{dy}{dx}+y^2+2x=0$ ?

Why? Click on this: solve dy&#47;dx &#43; y&#94;2 &#43; 2x &#61; 0 - Wolfram|Alpha
• Jul 6th 2010, 08:50 PM
math2009
Please check my solution, I doubt there are something wrongs in Attachment 18118
• Jul 6th 2010, 11:06 PM
mr fantastic
Quote:

Originally Posted by math2009
Please check my solution, I doubt there are something wrongs in Attachment 18118

Your method is wrong and your solution is wrong (did you even bother to check the solution by substituting it into the original DE?)

Although $y = \frac{1}{2x + a}$ satisfies $\frac{dy}{dx} + 2y^2 = 0$, it is also required to satisfy $\frac{dy}{dx} + 4 = 0$ and it doesn't. Similarly, the other part of your 'solution' has to satisfy both $\frac{dy}{dx} + 2y^2 = 0$ and $\frac{dy}{dx} + 4 = 0$ ....
• Jul 6th 2010, 11:48 PM
math2009
I also thought so before.
If a,b are variable but not constants, how about ?
• Jul 7th 2010, 12:11 AM
mr fantastic
Quote:

Originally Posted by math2009
I also thought so before.
If a,b are variable but not constants, how about ?

That wouldn't seem a very useful 'solution' to me.
• Jul 7th 2010, 12:33 AM
math2009
My opinion is : $\begin{bmatrix}x \\y \end{bmatrix} \rightarrow \begin{bmatrix}x(a,b) \\ y(a,b) \end{bmatrix}$

If equation#1 's solution is $E_1$ and equation#2 's is $E_2$ , then $E_1\cap E_2$ must fit both equations, is it right ?
And F(x, a, b) = 0 , it may simply solution
• Jul 7th 2010, 05:56 AM
mr fantastic
Quote:

Originally Posted by math2009
My opinion is : $\begin{bmatrix}x \\y \end{bmatrix} \rightarrow \begin{bmatrix}x(a,b) \\ y(a,b) \end{bmatrix}$

If equation#1 's solution is $E_1$ and equation#2 's is $E_2$ , then $E_1\cap E_2$ must fit both equations, is it right ?
And F(x, a, b) = 0 , it may simply solution

You are wrong and I have told you why. I am not spending any more time discussing this.
• Jul 8th 2010, 10:48 PM
math2009
mr fantastic , at first , thank you for discussion

There are two cases in this issue.

Case #1(constant) , as above mention, that's wrong.

Case #2(variables) , is there any proof ?