# Differential equations

1. Apr 12, 2008

### sara_87

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

i want to find the solution to:
dv/dx + 1/200 = 32/v

2. Relevant equations

3. The attempt at a solution

I dont know how to begin. what would be my first step?

2. Apr 12, 2008

### Hootenanny

Staff Emeritus
Can you identify which type of ODE it is? I.e. homogeneous/inhomogeneous, linear/non-linear etc.

3. Apr 12, 2008

### sara_87

first order, linear
isn't it?

4. Apr 12, 2008

### Hootenanny

Staff Emeritus
It is indeed, so which method does one usually use for solving first order, linear ODE's?

5. Apr 12, 2008

### sara_87

do multiply everything by v? or can we use the coefficient of v^(-1) to find the integrating factor?

6. Apr 12, 2008

### Hootenanny

Staff Emeritus
I would multiply it be v first, which puts the ODE into canonical form, and then find the IF.

7. Apr 12, 2008

### sara_87

are we allowed to have v*(dv/dx)?
because when i did i got:

[ve^(x/200)]dv/dx + (v/200)e^(x/200) = 32e^(x/200)

i don't think thats right

8. Apr 12, 2008

### Hootenanny

Staff Emeritus
Ohh dear, was I am thinking?! The ODE is separable, try writing the ODE in the form,

$$\frac{dv}{dx}=f(v)$$