# Thread: First Order Differential equation

1. ## First Order Differential equation

$\displaystyle (9x^2 + y -1)dx - (4y -x)dy = 0, y(0) = 1$

solve the given initial value problem and determine at least approximately where the solution is valid.

Can someone help me with this? im not quite sure how to really start this problem, I got that after integrating

$\displaystyle 3x^3 -x = 2y^2$

but im not sure where to go. The equations came out as exact after partial differentiating both with respect to each other x and y.

2. Originally Posted by p00ndawg
$\displaystyle (9x^2 + y -1)dx - (4y -x)dy = 0, y(0) = 1$

solve the given initial value problem and determine at least approximately where the solution is valid.

Can someone help me with this? im not quite sure how to really start this problem, I got that after integrating

$\displaystyle 3x^3 -x = 2y^2$

but im not sure where to go. The equations came out as exact after partial differentiating both with respect to each other x and y.
you have an exact equation here. now do you know how to proceed?

see post #2 here

3. Originally Posted by Jhevon
you have an exact equation here. now do you know how to proceed?
no, like what do i do with the initial value?

4. Originally Posted by Jhevon
you have an exact equation here. now do you know how to proceed?

see post #2 here
oh so i just plug it into the general solution?

5. Originally Posted by p00ndawg
oh so i just plug it into the general solution?
Yes. Since the general solution has the form $\displaystyle f\!\left(x,y\right)=C$, plugging in the initial condition yields $\displaystyle f\!\left(0,1\right)=C$. So you're particular solution would be $\displaystyle f\!\left(x,y\right)=f\!\left(0,1\right)$