- #1

rsera

- 5

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## Homework Statement

Find the general solution:

(y+1) dx + (4x - y) dy = 0

## Homework Equations

dy/dx + P(x)y = Q(x) (standard form)

e^(∫ P(x) dx) (integrating factor)

## The Attempt at a Solution

This exercise is in the chapter on linear equations, making non-exact equations exact.

So I know I need to put it into the form:

dy/dx + P(x)y = Q(x)

So that I can find the Integrating Factor:

e^( ∫ P(x) dx)

Then multiply through by the Integrating Factor and solve the resulting exact equation.

My problem with this one has been getting it into that standard form.

If I divide by dx and rearrange, I get:

(4x - y) dy/dx + (y+1) = 0

Then divide by (4x - y)

dy/dx + (y + 1) / (4x - y) = 0

However, this does not match the standard form, because it is not a function of x times y.

I know what to do once it's in standard form, I'm just having troubles getting to that point. Any clue as to what trick to use to get it to standard form would be appreciated. Thanks!

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