# Finding F(x)=G(x)+H(y)=K

1. Sep 6, 2009

### hardatwork

1. The problem statement, all variables and given/known data
The differential equation dy/dx= 35/(y1/8+25x2y1/8 has an implicit general solution of the form F(x,y)=K. In fact, because the differential equation is separable, we can define the solution curve implicitly by the form F(x)=G(x)+H(y)=K.
Find such solution and then give the related functions requested.

2. Relevant equations

3. The attempt at a solution
dy/dx=35/(y1/8(1+25x2)
1+25x2/35 dx=y1/8dy
1/35$$\int1+25x^2 dx$$=$$\int y^(1/8) dy$$
x+25x3/105=8/9y9/8
105(8/9y9/8)-x-253=K
so G(x)=x+25x3 and H(y)=8/9y9/8

2. Sep 6, 2009

### hardatwork

The problem is that this is incorrect and I dont know what I did wrong. Can someone see my mistake. Thank You in advance

3. Sep 6, 2009

### Subdot

The bolded line is where you went wrong. Look carefully at what you did. It may be easier to see if you wrote it out "properly:"

$$\frac{dy}{dx} = \frac{35}{y^{1/8} + y^{1/8}25x^2}$$

$$\frac{dy}{dx} = \frac{35}{y^{1/8}(1 + 25x^2)}$$

Edit: I'm assuming the bolded line really reads ((1+25x2)/35)dx=y1/8dy

Last edited by a moderator: Sep 7, 2009
4. Sep 6, 2009

### hardatwork

So when I separate the variables it should be
y1/8dy=$$35/1+25x^2 dx$$

5. Sep 6, 2009

### Subdot

Assuming you mean y1/8dy=(35/(1+25x2))dx, then yes, that is correct. It is more easily read as (35dx)/(1+25x2) or 35dx/(1+25x2) though, imo.

6. Sep 6, 2009

### hardatwork

Okay. Thank You