The solution of the differential equation $\frac{y dx + x dy}{y dx - x dy} = \frac{x^{2} e^{xy}}{y^{4}} $ satisfying $y(0) = 1$, is :
- $x^3 = 3y^3 (1 - e^{-xy} )$
- $x^3 = 3y^3 ( - 1 + e^{xy} )$
- $x^3 = 3y^3 (1 - e^{xy} )$
- $x^3 = 3y^3 (- 1 + e^{-xy} )$
The Correct Option is A
Solution and Explanation
Top Questions on General and Particular Solutions of a Differential Equation
- Let \( \alpha, \beta (\alpha \neq \beta) \) be the values of m, for which the equations \(x + y + z = 1\), \(x + 2y + 4z = m\), and \(x + 4y + 10z = m^2\) have infinitely many solutions. Then the value of \(\sum_{n=1}^{10} (n^4 + n^8)\) is equal to:
- JEE Main - 2025
- Mathematics
- General and Particular Solutions of a Differential Equation
- If y = f(x) is solution of differential equation \((x^2 - 1) dy = ((x^3 + 1) + \sqrt{(1 - x^2)}dx \) and \(y(0) = 2\) then find \(y(\frac{1}2)\)
- JEE Main - 2024
- Mathematics
- General and Particular Solutions of a Differential Equation
If the roots of $\sqrt{\frac{1 - y}{y}} + \sqrt{\frac{y}{1 - y}} = \frac{5}{2}$ are $\alpha$ and $\beta$ ($\beta > \alpha$) and the equation $(\alpha + \beta)x^4 - 25\alpha \beta x^2 + (\gamma + \beta - \alpha) = 0$ has real roots, then a possible value of $y$ is:
- AP EAMCET - 2024
- Mathematics
- General and Particular Solutions of a Differential Equation
- Find the integrating factor of the differential equation \( \sin x \frac{dy}{dx} - y \cos x = 1 \):
- AP EAMCET - 2024
- Mathematics
- General and Particular Solutions of a Differential Equation
- If five-digit numbers are formed from the digits 0, 1, 2, 3, 4 using every digit exactly only once, then the probability that a randomly chosen number from those numbers is divisible by 4 is
- AP EAMCET - 2024
- Mathematics
- General and Particular Solutions of a Differential Equation
Questions Asked in JEE Main exam
- If the coefficient of \( x \) in the expansion of \[ (ax^2 + bx + c)(1 - 2x)^{26} \] is \(-56\) and the coefficients of \( x^2 \) and \( x^3 \) are both zero, then \( a + b + c \) is equal to
- JEE Main - 2026
- Binomial theorem
The equivalent resistance between the points \(A\) and \(B\) in the given circuit is \[ \frac{x}{5}\,\Omega. \] Find the value of \(x\).
- JEE Main - 2026
- Current electricity
Method used for separation of mixture of products (B and C) obtained in the following reaction is:
- JEE Main - 2026
- p -Block Elements
- Consider light travelling from a medium A to medium B separated by a plane interface. If the light undergoes total internal reflection during its travel from medium A to B and the speed of light in media A and B are \(2.4 \times 10^8\) m/s and \(2.7 \times 10^8\) m/s, respectively, then the value of critical angle is :
- JEE Main - 2026
- Newtons Laws of Motion
In the following \(p\text{–}V\) diagram, the equation of state along the curved path is given by \[ (V-2)^2 = 4ap, \] where \(a\) is a constant. The total work done in the closed path is:
- JEE Main - 2026
- Thermodynamics
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