Question

what is difference between first second third forth and fifth ordinary deffertial equation
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Answer 1

Answer:

Differential Equations

In Mathematics, a differential equation is an equation that contains one or more functions with its derivatives. The derivatives of the function define the rate of change of a function at a point. It is mainly used in fields such as physics, engineering, biology and so on. The primary purpose of the differential equation is the study of solutions that satisfy the equations and the properties of the solutions.

Step-by-step explanation:

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Answer 2

Answer: First order differential equation:

The order of highest derivative in case of first order differential equations is 1. A linear differential equation has order 1. In case of linear differential equations, the first derivative is the highest order derivative.

dydx+Py=Q

P and Q are either constants or functions of the independent variable only.

This represents a linear differential equation whose order is 1.

Example: dydx+(x2+5)y=x5

This also represents a First order Differential Equation.

Second Order Differential Equation:

When the order of the highest derivative present is 2, then it is a second order differential equation.

Example: d2ydx2+(x3+3x)y=9

In this example, the order of the highest derivative is 2. Therefore, it is a second order differential equation.

Degree of Differential Equation:

The degree of the differential equation is represented by the power of the highest order derivative in the given differential equation.

The differential equation must be a polynomial equation in derivatives for the degree to be defined.

Example 1:- d4ydx4+(d2ydx2)2–3dydx+y=9

Here, the exponent of the highest order derivative is one and the given differential equation is a polynomial equation in derivatives. Hence, the degree of this equation is 1.

Example 2: [d2ydx2+(dydx)2]4=k2(d3ydx3)2

The order of this equation is 3 and the degree is 2 as the highest derivative is of order 3 and the exponent raised to the highest derivative is 2.

Step-by-step explanation: