Differential equation is an equation of a function with its derivatives. Differential equation is expressed in the form of y = f(x), where y is the function of a variable x. The highest derivative present in the equation is the order of differential equation. Differential equation can be classified depending upon the order of derivative,

- First order differential equation,
- Second order differential equation,
- Third order differential equation.

Step 2 : Separate the x variable in one side and y variable on other side.

Step 3 : By integrating on both the sides, we will get differential equation.

Given below are the problems for your references.

### Solved Examples

**Question 1:**Solve the differential equation :

$\frac{dy}{dx}$ = 7x - 3 ?

**Solution:**

Step 1 : Given, $\frac{dy}{dx}$ = 7x - 3

Step 2 : Separating both the variables,

dy = (7x - 3)dx

Step 3 : By integrating on both sides,

$\int dy = \int (7x - 3)dx$

y = 7 $\int xdx - 3 \int dx$

y = 7 $\frac{x^{2}}{2}$ - 3x

y = $\frac{7x^{2}}{2}$ - 3x + c

Therefore, the differential equation of $\frac{dy}{dx}$ = 7x - 3 is y = $\frac{7x^{2}}{2}$ - 3x + c, where c

_{}is the arbitrary constant.

**Question 2:**Solve the differential equation :

$\frac{dy}{dx}$ = -x$e^{x}$ ?

**Solution:**

Step 1 : Given, $\frac{dy}{dx}$ = -x$e^{x}$

Step 2 : Separating both the variables,

$dy = -xe^{x}dx$

Step 3 : By integrating on both sides,

$\int dy = \int -xe^{x}dx$

$y = - xe^{x} + \int e^{x}dx + c$

$y = (1 - x)e^{x} + c$

Therefore, the differential equation of $\frac{dy}{dx}$ = -x$e^{x}$ is $y = (1 - x)e^{x} + c$, where c is the arbitrary constant.