VARIABLE SEPARABLE DIFFERENTIAL EQUATIONS PROBLEMS

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 :

If F is the constant force generated by the motor of an automobile of mass M , its velocity V is given by

where k is a constant. Express V in terms of t given that V = 0 when t = 0.

Solution :

Problem 5 :

The velocity v , of a parachute falling vertically satisfies the equation

where g and k are constants. If v and x are both initially zero, find v in terms of x .

Solution :

Solving for C :

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