Solving Differential Equations: Step-by-Step Guide for Homework

[sara_87]

Homework Statement

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

Homework Equations

The Attempt at a Solution

I don't know how to begin. what would be my first step?

 

[Hootenanny]

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

 

[sara_87]

first order, linear
isn't it?

 

[Hootenanny]

first order, linear
isn't it?

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

 

[sara_87]

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

 

[Hootenanny]

do multiply everything by v?

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

 

[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 that's right

 

[Hootenanny]

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

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

Sorry about that, I had a stupid moment

 

[sara_87]

its ok i always have stupid moments.
Thank you very much u've been much help.