Separable Differential Equations
Definition and Solution of a Separable Differential
Equation
A differential equation is called
separable
if it can be written as
Steps To Solve a Separable Differential Equation
To solve a separable differential equation

Get all the y's on the left
hand side of the equation and all of the x's
on the right hand side.

Integrate both sides.

Plug in the given values to find the constant of
integration (C)

Solve for y
Example:
Solve
dy/dx = y(3  x); y(0 )= 5

dy/y = (3  x) dx

lny = 3x  x^{2}/2 + C

ln5 = 0 + 0 + C
C = ln5

Exercises:

dy/dx = x/y; y(0) = 1

dy/dx = x(x+1); y(1) = 1

2xy + dy/dx = x; y(0) = 2
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