Question:
General Solution of the differential equation:
\(cos\,x(1+cos\,y)dx-sin\,y(1+sin\,x)dy=0\) is:
General Solution of the differential equation:
\(cos\,x(1+cos\,y)dx-sin\,y(1+sin\,x)dy=0\) is:
\(cos\,x(1+cos\,y)dx-sin\,y(1+sin\,x)dy=0\) is:
Updated On: Jun 23, 2024
- \((1+cos\,x)(1+sin\,y)\)= c
- \(1+sin\,x+cos\,y=c\)
\((1+sin\,x)(1+cos\,y)=c\)
- \(1+sin\,x.cos\,y=c\)
Hide Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
The correct option is (C): \((1+sin\,x)(1+cos\,y)=c\)
Was this answer helpful?
1
0
Top Questions on Differential equations
- Let \( y = f(x) \) be the solution of the differential equation\[\frac{dy}{dx} + \frac{xy}{x^2 - 1} = \frac{x^6 + 4x}{\sqrt{1 - x^2}}, \quad -1 < x < 1\] such that \( f(0) = 0 \). If \[6 \int_{-1/2}^{1/2} f(x)dx = 2\pi - \alpha\] then \( \alpha^2 \) is equal to __________.
- JEE Main - 2025
- Mathematics
- Differential equations
- If \( x = f(y) \) is the solution of the differential equation \[ (1 + y^2) + (x - 2e^{\tan^{-1}y}) \frac{dy}{dx} = 0, \quad y \in \left( -\frac{\pi}{2}, \frac{\pi}{2} \right), \] with \( f(0) = 1 \), then \( f\left( \frac{1}{\sqrt{3}} \right) \) is equal to:
- JEE Main - 2025
- Mathematics
- Differential equations
- Let \( f(x) \) be a real differentiable function such that \( f(0) = 1 \) and \( f(x + y) = f(x)f'(y) + f'(x)f(y) \) for all \( x, y \in \mathbb{R} \). Then \( \sum_{n=1}^{100} \log_e f(n) \) is equal to :
- JEE Main - 2025
- Mathematics
- Differential equations
- Let \( x = x(y) \) be the solution of the differential equation \( y^2 dx + \left( x - \frac{1}{y} \right) dy = 0 \). If \( x(1) = 1 \), then \( x\left( \frac{1}{2} \right) \) is :
- JEE Main - 2025
- Mathematics
- Differential equations
Let \( f : \mathbb{R} \to \mathbb{R} \) be a twice differentiable function such that \( f(x + y) = f(x) f(y) \) for all \( x, y \in \mathbb{R} \). If \( f'(0) = 4a \) and \( f \) satisfies \( f''(x) - 3a f'(x) - f(x) = 0 \), where \( a > 0 \), then the area of the region R = {(x, y) | 0 \(\leq\) y \(\leq\) f(ax), 0 \(\leq\) x \(\leq\) 2\ is :
- JEE Main - 2025
- Mathematics
- Differential equations
View More Questions
Questions Asked in MHT CET exam
- What is the oxidation state of Fe in \( \mathrm{Fe_3O_4} \)?
- MHT CET - 2024
- States of matter
- The number of ways of distributing \( 500 \) dissimilar boxes equally among \( 50 \) persons is
- MHT CET - 2024
- Permutations
- A committee of 11 members is to be formed out of 8 males and 5 females. If \( m \) is the number of ways the committee is formed with at least 6 males and \( n \) is the number of ways with at least 3 females, then:
- MHT CET - 2024
- Combinations
- Two monkeys off mass 10 kg and 8 kg are moving along a vertical light rope the former climbing up with an acceleration of 2 m/second square while the latter coming down with a uniform velocity of 2 m/sec square find the tension in the rope at the fixed support
- MHT CET - 2024
- tension
- Which of the following is ferromagnetic:
- MHT CET - 2024
- Magnetism and matter
View More Questions
Concepts Used:
General Solutions to Differential Equations
A relation between involved variables, which satisfy the given differential equation is called its solution. The solution which contains as many arbitrary constants as the order of the differential equation is called the general solution and the solution free from arbitrary constants is called particular solution.
For example,
Read More: Formation of a Differential Equation