# Integratable combination question

1. Jan 17, 2007

### snowJT

1. The problem statement, all variables and given/known data

Obtain the general solution of $$2xydy - 6y^2dy + 8xdx + y^2dx = 0$$

2. The attempt at a solution

$$2xydy - 6y^2dy + 8xdx + y^2dx = 0$$

$$2xydy + y^2dx = 6y^2dy - 8xdx$$

$$\intd(xy^2) = \int6y^2dy - 8xdx$$

$$xy^2 = \frac{6y^3}{3} - \frac{8x^2}{2}+C$$

$$xy^2 = 2y^3 - 4x^2+C$$

3. The problem statement, all variables and given/known data

Find the particular solution of the DE that satisfies the condition y = 5 when x = 1

4. The attempt at a solution

$$xy^2 = 2y^3 - 4x^2+C$$

$$(5)^2 = 2(5)^3 - 4+C$$

$$25 = 250 - 4+C$$

$$C = -221$$

Does all of this look right to you? I'm not so sure about the last part?

2. Jan 17, 2007

### JJ420

i think it looks good....but i am always wrong about these things....can someone else see if this is correct or not

3. Jan 17, 2007

### Dick

It's right. Did you really tex all of that up to get someone to check your arithmetic?