DIFFERENTIAL EQUATIONS VARIABLE SEPARABLE METHOD

What is variable separable method ?

Finding a solution to a first order differential equation will be simple if the variables in the equation can be separated.

To use the method of variable separable, we have to follow the procedure given below.

Step 1 :

An equation of the form

f₁(x) g₁(y) dx + f₂(x) g₂(y) dy = 0

is called an equation with variable separable or simply a separable equation.

Step 2 :

Collect the variable x and dx one side and collect variables y, dy in other side of the equal sign.

Step 3 :

Then integrate on both sides.

Problem 1 :

Solve

Solution :

Problem 2 :

Solve

Solution :

Problem 3 :

Solve

Solution :

Problem 4 :

Solve

Solution :

Problem 5 :

Solve

Solution :

Problem 6 :

Solve

(y dx - x dy) cot (x/y) = ny² dx

Solution :

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