HOMOGENEOUS DIFFERENTIAL EQUATIONS EXAMPLES

If M (x, y) dx + N (x, y) dy = 0 is a homogeneous equation, then the change of variable

y = vx

transforms into a separable equation in the variables v and x.

How to solve homogenous differential equation ?

Step 1 :

Since the given differential equation is not solvable using the method of variable separable, we will use homogenous.

Step 2 :

Put y = vx

dy/dx = v + x (dv/dx)

Apply the value of dy/dx in the given question.

Step 3 :

Using the method of variable separable, we can solve this equation.

The detailed examples are shown below.

Solve the following differential equation.

Problem 1 :

Solution :

Applying the initial value, we get

Problem 2 :

(x² + y²) dy = xy dx

It is given that y(1) = 1 and y(x₀) = e. Find the value of x₀

Solution :

(x² + y²) dy = xy dx

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