Determine order and degree(if defined)of differential equation \(\frac{d^4y}{dx^4}\)+sin(y''')=0
Determine order and degree(if defined)of differential equation \(\frac{d^4y}{dx^4}\)+sin(y''')=0
Solution and Explanation
\(\frac{d^4y}{dx^4}\)+sin(y''')=0
⇒y''' '+sin(y''')=0
The highest order derivative present in the differential equations is y''' '.Therefore, its order is four.
The given differential equation is not a polynomial equation in its derivatives. Hence, its degree is not defined.
Top Questions on Differential equations
- Solve the differential equation: \[ x \cos\left(\frac{y}{x}\right) \frac{dy}{dx} = y \cos\left(\frac{y}{x}\right) + x \]
- CBSE CLASS XII - 2025
- Mathematics
- Differential equations
- Find the particular solution of the differential equation \( \frac{dy}{dx} - \frac{y}{x} + \csc\left(\frac{y}{x}\right) = 0 \); given that \( y = 0 \), when \( x = 1 \).
- CBSE CLASS XII - 2025
- Mathematics
- Differential equations
- The sum of the order and degree of the differential equation \[ \left( 1 + \left( \frac{dy}{dx} \right)^2 \right) \frac{d^2y}{dx^2} = \left( \frac{dy}{dx} \right)^3 \] is:
- CBSE CLASS XII - 2025
- Mathematics
- Differential equations
- The integrating factor of the differential equation \( \frac{dx}{dy} = \frac{x \log x}{2 \log x - y} \) is:
- CBSE CLASS XII - 2025
- Mathematics
- Differential equations
- The sum of the order and degree of the differential equation \[ \left( 1 + \left( \frac{dy}{dx} \right)^2 \right) \frac{d^2y}{dx^2} = \left( \frac{dy}{dx} \right)^3 \] is:
- CBSE CLASS XII - 2025
- Mathematics
- Differential equations
Questions Asked in CBSE CLASS XII exam
- Determine those values of $x$ for which $f(x) = \frac{2}{x} - 5$, $x \ne 0$ is increasing or decreasing.
- CBSE CLASS XII - 2025
- Functions
- Agro-startups and rural enterprises are becoming increasingly vital for rural development in India. They address the critical challenges faced by rural sector in India. These ventures bring in technological innovations such as precision farming, IT-based monitoring system and data-driven decision making tools that enhance productivity and resource efficiency. By streamlining supply chains and creating direct market linkages, they ensure better pricing for farmers and reduce dependency on traditional intermediaries. Such enterprises contribute actively to employment generation in the rural areas. The government has demonstrated a continuous policy and financial support for agri-startups and entrepreneurs through various programs like RKVY-RAFTAAR, the Agri- infrastructure fund and Agri-SURE.
On the basis of given text and common understanding, answer the following questions:- CBSE CLASS XII - 2025
- Rural Development
Read the following text carefully:
Union Food and Consumer Affairs Minister said that the Central Government has taken many proactive steps in the past few years to control retail prices of food items. He said that the government aims to keep inflation under control without compromising the country’s economic growth. Retail inflation inched up to a three-month high of 5.55% in November 2023 driven by higher food prices. Inflation has been declining since August 2023, when it touched 6.83%. 140 new price monitoring centres had been set up by the Central Government to keep a close watch on wholesale and retail prices of essential commodities. The Government has banned the export of many food items like wheat, broken rice, non-basmati white rice, onions etc. It has also reduced import duties on edible oils and pulses to boost domestic supply and control price rise. On the basis of the given text and common understanding,
answer the following questions:- CBSE CLASS XII - 2025
- Government Budget and the Economy
- Distinguish between Physical Capital and Human Capital.
- CBSE CLASS XII - 2025
- Human Capital Formation
- “In the recent Budget the Government allocated funds for construction of new metro lines in smart cities to improve public transportation and reduce pollution.”
Identify the nature of government expenditure \& its objective.- CBSE CLASS XII - 2025
- Government Budget and the Economy
Concepts Used:
Order and Degree of Differential Equation
The equation that helps us to identify the type and complexity of the differential equation is the order and degree of a differential equation.
The Order of a Differential Equation:
The highest order of the derivative that appears in the differential equation is the order of a differential equation.
The Degree of a Differential Equation:
The highest power of the highest order derivative that appears in a differential equation is the degree of a differential equation. Its degree is always a positive integer.
For examples:
- 7(d4y/dx4)3 + 5(d2y/dx2)4+ 9(dy/dx)8 + 11 = 0 (Degree - 3)
- (dy/dx)2 + (dy/dx) - Cos3x = 0 (Degree - 2)
- (d2y/dx2) + x(dy/dx)3 = 0 (Degree - 1)