# Differential equations

1. Homework Statement

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

2. Homework Equations

3. The Attempt at a Solution

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

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

first order, linear
isn't it?

Hootenanny
Staff Emeritus
Gold Member
first order, linear
isn't it?
It is indeed, so which method does one usually use for solving first order, linear ODE's?

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

Hootenanny
Staff Emeritus
Gold Member
do multiply everything by v?
I would multiply it be v first, which puts the ODE into canonical form, and then find the IF.

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

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

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