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

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

2. Integrate both sides.
   

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

4. Solve for y
   

Example:

Solve 

dy/dx = y(3 - x);   y(0 )= 5

1. dy/y = (3 - x) dx
   
   

2.  
   
     lny = 3x - x²/2 + C
   
   

3. ln5 = 0 + 0 + C  
   
   C = ln5
   
   

4. 

    
   

Exercises:  

1. dy/dx = x/y;   y(0) = 1
   

2. dy/dx = x(x+1);  y(1) = 1 
   

3. 2xy + dy/dx = x;  y(0) = 2

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