# Thread: [SOLVED] Ingegrating factors

1. ## [SOLVED] Ingegrating factors

Assign to each of the following differential equations the integrating factor/s (if there are any listed, multiple answers possible).

A) (1 + y^2)/x^2 + y′ = 0 I) μ = 1/(1 + y^2)

B) y/(4 + x) + y′ = 0 II) μ = 1/y

C) 1 + (1 + x)yy′ = 0 III) μ = 4 + x

A= I
B= III
C= II

2. Originally Posted by ronaldo_07
A= I
B= III
C= II

Can anyone confirm if this is correct?

3. Originally Posted by ronaldo_07
Assign to each of the following differential equations the integrating factor/s (if there are any listed, multiple answers possible).

A) (1 + y^2)/x^2 + y′ = 0 I) μ = 1/(1 + y^2)

B) y/(4 + x) + y′ = 0 II) μ = 1/y

C) 1 + (1 + x)yy′ = 0 III) μ = 4 + x

A= I
B= III
C= II
Check on what you post in (A) - it's not linear
(B) is correct and check on your post on (C) because it has an integrating factor but not one that is list here.

4. A- If its not linear then there are no integrating factors?

5. Originally Posted by ronaldo_07
A- If its not linear then there are no integrating factors?
Good point. Usually integrating factor are used for linear ODE but if you write your equation

$\displaystyle \frac{1+y^2}{x} \; dx + dy = 0$

then ask for $\displaystyle \mu$ such that your equation becomes

$\displaystyle \mu \frac{1+y^2}{x} \; dx + \mu\; dy = dF = 0$, then yes, you are correct.

6. What would be the integrating factor for for C, if it is not in the list?

7. Originally Posted by 1234567
What would be the integrating factor for for C, if it is not in the list?
$\displaystyle 1 + (1 + x)y y' = 0$

if you write the equation as

$\displaystyle dx + (1 + x)y dy = 0$

then it would be

$\displaystyle \mu = \frac{1}{1+x}$

8. Originally Posted by danny arrigo
c) $\displaystyle 1 + (1 + x)yy′ = 0$

if you write the equation as

$\displaystyle dx + (1 + x)y dy = 0$

then it would be

$\displaystyle \mu = \frac{1}{1+x}$

Thak for that, was not really sure what it could have been