Learn Class 12 Math - Differential Equations

The term differential equation refers to an equation that involves the dependent variable, independent variable, and another differential dependent variable coefficient. The differential equation is dy/dx or d2y/d2x.

Order of differential equation

• It is from the highest order derivative in the differential equation.

Degree of differential equation

• The highest degree of the higher-order derivative is when all the coefficients are made free of radicals.

Methods of solving differential equations

Many methods will help solve the first-order, second-order, and differential equations. Such methods are:

• Linear Differential Equations
• Homogeneous Differential Equations
• Differential equations with variable separable

Solved Problems

Question 1: Determine the request and degree for y' + 5y = 0

Arrangement:

Given, differential condition y' + 5y = 0

Request = 1 (Highest request subordinate is y')

Degree = 1 (Highest power raised to y')

Question 2: Check that the y = cos x + C is an answer of y′ + sin x = 0.

Arrangement:

Given, y = cos x + C

Separating the two sides as for x, we get,

y' = d/dx(cos x + C)

y' = - Sin x

Subbing the upsides of y' in the given differential conditions, y′ + sin x = 0, we get;

= y' + sin x

= - sin x + sin x

= 0

Here, y = cos x + C is an answer of y′ + sin x = 0.