Question:
The order of the differential equation $\left(\frac{d^{3}\, y }{dx^{3}}\right)^{2} + \left(\frac{d^{2}\,y}{dx}\right)^{2} + \left(\frac{dy}{dx}\right)^{5} = 0 $ is
The order of the differential equation $\left(\frac{d^{3}\, y }{dx^{3}}\right)^{2} + \left(\frac{d^{2}\,y}{dx}\right)^{2} + \left(\frac{dy}{dx}\right)^{5} = 0 $ is
Updated On: Jun 8, 2024
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Solution and Explanation
We have,
$\left(\frac{d^{3}\, y}{d x^{3}}\right)^{2}+\left(\frac{d^{2} \,y}{d x^{2}}\right)^{2}+\left(\frac{d y}{d x}\right)^{5}=0$
Since, the highest order derivative is $\frac{d^{3} y}{d x^{3}}$
$\therefore$ Order of the given differential equation is $3$
$\left(\frac{d^{3}\, y}{d x^{3}}\right)^{2}+\left(\frac{d^{2} \,y}{d x^{2}}\right)^{2}+\left(\frac{d y}{d x}\right)^{5}=0$
Since, the highest order derivative is $\frac{d^{3} y}{d x^{3}}$
$\therefore$ Order of the given differential equation is $3$
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Concepts Used:
Differential Equations
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.
Orders of a Differential Equation
First Order Differential Equation
The first-order differential equation has a degree equal to 1. All the linear equations in the form of derivatives are in the first order. It has only the first derivative such as dy/dx, where x and y are the two variables and is represented as: dy/dx = f(x, y) = y’
Second-Order Differential Equation
The equation which includes second-order derivative is the second-order differential equation. It is represented as; d/dx(dy/dx) = d2y/dx2 = f”(x) = y”.
Types of Differential Equations
Differential equations can be divided into several types namely
- Ordinary Differential Equations
- Partial Differential Equations
- Linear Differential Equations
- Nonlinear differential equations
- Homogeneous Differential Equations
- Nonhomogeneous Differential Equations