Question:
An integrating factor of the differential equation $xdy - ydx + x^2e^xdx = 0$ is
An integrating factor of the differential equation $xdy - ydx + x^2e^xdx = 0$ is
Updated On: Jun 7, 2024
- $\frac{1}{x}$
- $log\sqrt{1+x^{2}}$
- $\sqrt{1+x^{2}}$
- $x$
Hide Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Given differential equation i
$\mid x d y-y d x+x^{2} e^{x} d x=0$
$\Rightarrow x d y+d x\left(x^{2} e^{x}-y\right)=0$
$\Rightarrow \frac{d y}{d x}-\frac{y}{x}=-x e^{x}$
$\therefore IF =e^{\int P d x}=e^{\int-\frac{1}{x} d x}$
$=e^{-\log x} $
$\mid x d y-y d x+x^{2} e^{x} d x=0$
$\Rightarrow x d y+d x\left(x^{2} e^{x}-y\right)=0$
$\Rightarrow \frac{d y}{d x}-\frac{y}{x}=-x e^{x}$
$\therefore IF =e^{\int P d x}=e^{\int-\frac{1}{x} d x}$
$=e^{-\log x} $
Was this answer helpful?
0
0
Top Questions on Differential equations
- If \[\frac{dx}{dy} = \frac{1 + x - y^2}{y}, \quad x(1) = 1,\]then $5x(2)$ is equal to:
- JEE Main - 2024
- Mathematics
- Differential equations
- Let $\alpha$ be a non-zero real number. Suppose $f : \mathbb{R} \to \mathbb{R}$ is a differentiable function such that $f(0) = 2$ and \[\lim_{x \to \infty} f(x) = 1.\]If $f'(x) = \alpha f(x) + 3$, for all $x \in \mathbb{R}$, then $f(-\log 2)$ is equal to ________ .
- JEE Main - 2024
- Mathematics
- Differential equations
- Let\(f(x) = |2x^2 + 5|x - 3|, x \in \mathbb{R}\). If \(m\) and \(n\) denote the number of points were \(f\)is not continuous and not differentiable respectively, then\(m + n\)is equal to:
- JEE Main - 2024
- Mathematics
- Differential equations
- Let \( y = y(x) \) be the solution of the differential equation \[\left( 1 + x^2 \right) \frac{dy}{dx} + y = e^{\tan^{-1}x}, \, y(1) = 0.\]Then \( y(0) \) is:
- JEE Main - 2024
- Mathematics
- Differential equations
- Let \( y = y(x) \) be the solution of the differential equation \[\left( 2x \log_e x \right) \frac{dy}{dx} + 2y = \frac{3}{x} \log_e x, \, x>0 \, \text{and} \, y(e^{-1}) = 0.\] Then, \( y(e) \) is equal to:
- JEE Main - 2024
- Mathematics
- Differential equations
View More Questions
Questions Asked in KEAM exam
- A Spherical ball is subjected to a pressure of 100 atmosphere. If the bulk modulus of the ball is 1011 N/m2,then change in the volume is:
- KEAM - 2023
- mechanical properties of solids
- Two identical solid spheres,each of radius 10cm,are kept in contact. If the mass of inertia of this system about the tangent passing through the point of contact is 0. Then mass of each sphere is:
- KEAM - 2023
- System of Particles & Rotational Motion
- The value of a(≠0) for which the equation \(\frac{1}{2}(x-2)^2+1=\sin(\frac{a}{x})\) holds is/are
- KEAM - 2023
- Trigonometric Functions
- \(∫xlog(1+x^2)dx=\)?
- KEAM - 2023
- Integration by Parts
- A uniform thin rod of mass 3kg has a length of 1m. If a point mass of 1kg is attached to it at a distance of 40cm from its center,the center of mass shifts by a distance of:
- KEAM - 2023
- System of Particles & Rotational Motion
View More Questions
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