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## Homework Statement

Solv the simultaneous homogenous differential equation

[tex]\begin{cases} dy/dx + dz/dx + 3y = 0 \\ dy/dx - y + z = 0 \end{cases}[/tex]

## Homework Equations

## The Attempt at a Solution

(from eq 2),

[tex]dy/dx = y - z [/tex] --- eq (3)

(substituting eq 3 in eq 1),

[tex]\therefore dz/dx = z - 4y [/tex]

[tex]\therefore dz = (z - 4y)dx[/tex]

[tex]but, dy/(y - z) = dx[/tex]

[tex]\therefore dz = \frac{(z - 4y)}{(y - z)} dy[/tex]

[tex]\therefore dz = \frac{(z - 4y)}{(y - z)} dy[/tex]

I am now having trouble separating the variables. Help would be appreciated.

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