# Show that the following differential equation is homogeneous and then find its solution x(x + y)...

## Question:

Show that the following differential equation is homogeneous and then find its solution

{eq}x (x + y) \frac {dy}{dx} = y (x - y) {/eq}

## Homogeneous Differential Equation :

Here, first of all, we will verify that the given differential equation is a homogeneous differential equation, for that we will perform a test. Then after the given differential equation will be converted into a variable -separable differential equation by the help of substitution.

$$\int_{}^{} \; x^{n} \; dx = \frac {x^{n+1}}{n+1} + C $$

$$\int_{}^{} \; \frac {dx}{x} = \ln(|x|) + C $$

$$\text {Here} \; C \; \text {is the constant of integration.} $$

## Answer and Explanation: 1

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View this answer$$\text {The differential equation which we have to solve is given as -} $$

$$x \; \biggr(x +y \biggr) \; \frac {dy}{dx} = y \; (x -y) $$

$$\Righ...

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Chapter 15 / Lesson 2Explore the separation of variables in differential equations. Study the steps involved in the method of separation of variables with examples in each step.