(A) For a linear differential equation of the form $\frac{dy}{dx} + P(x)y = Q(x)$,the integrating factor $(IF)$ is defined as $IF = e^{\int P(x) dx}$.

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(A) For a linear differential equation of the form $\frac{dy}{dx} + P(x)y = Q(x)$,the integrating factor $(IF)$ is defined as $IF = e^{\int P(x) dx}$.Let $u = e^{\int P(x) dx}$.Then,$\frac{du}{dx} = e^{\int P(x) dx} \cdot \frac{d}{dx}(\int P(x) dx) = u \cdot P(x)$.This implies $\frac{du}{dx} - P(x)u = 0$.Since the integrating factor $u$ satisfies this equation,the correct option is $\frac{dy}{dx} - P(x)y = 0$.

Class 12 Mathematics Differential Equations Linear differential equations

Medium

The integrating factor of the linear differential equation $\frac{dy}{dx} + P(x)y = Q(x)$ is a solution of the differential equation:

AP EAMCET 2022 All AP EAMCET

A
$\frac{dy}{dx} - P(x)y = 0$
B
$\frac{dy}{dx} + P(x)y = 0$
C
$\frac{dy}{dx} - \frac{y}{x} = P(x)$
D
$\frac{dy}{dx} + \frac{x}{y} = P(x)$

Explore More

Browse All

Question Bank

All Subjects

Class 12 Questions

Class 12

Mathematics Questions

Chapter

Differential Equations

Subtopic

Linear differential equations

Previous Year

AP EAMCET 2022 Paper All AP EAMCET years →

The general solution of the differential equation $\frac{dy}{dx} = y \tan x - y^2 \sec x$ is

DifficultMHT CET 2024

View Solution

If the solution of the differential equation $x \frac{dy}{dx} + y = x e^x$ is $xy = e^x \phi(x) + C$, then $\phi(x)$ is equal to

DifficultWBJEE 2016

View Solution

The solution of $\frac{dy}{dx} + y = e^x$ is

EasyAP EAMCET 2001

View Solution

Let $y = y(x)$ be the solution of the differential equation $\frac{dy}{dx} + 2y = f(x)$,where $f(x) = \begin{cases} 1, & x \in [0, 1] \\ 0, & \text{otherwise} \end{cases}$. If $y(0) = 0$,then $y\left(\frac{3}{2}\right)$ is

DifficultJEE MAIN 2018

View Solution

Let $f : R \rightarrow R$ be a differentiable function such that $f^{\prime}(x)+f(x)=\int \limits_0^2 f(t) dt$. If $f(0)=e^{-2}$,then $2f(0)-f(2)$ is equal to $.........$.

DifficultJEE MAIN 2023

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

The integrating factor of the linear differential equation $\frac{dy}{dx} + P(x)y = Q(x)$ is a solution of the differential equation:

Similar Questions

The general solution of the differential equation $\frac{dy}{dx} = y \tan x - y^2 \sec x$ is

If the solution of the differential equation $x \frac{dy}{dx} + y = x e^x$ is $xy = e^x \phi(x) + C$, then $\phi(x)$ is equal to

The solution of $\frac{dy}{dx} + y = e^x$ is

Let $y = y(x)$ be the solution of the differential equation $\frac{dy}{dx} + 2y = f(x)$,where $f(x) = \begin{cases} 1, & x \in [0, 1] \\ 0, & \text{otherwise} \end{cases}$. If $y(0) = 0$,then $y\left(\frac{3}{2}\right)$ is

Let $f : R \rightarrow R$ be a differentiable function such that $f^{\prime}(x)+f(x)=\int \limits_0^2 f(t) dt$. If $f(0)=e^{-2}$,then $2f(0)-f(2)$ is equal to $.........$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module