(A) Given the differential equation: $x^2 + y^2 \frac{dy}{dx} = 4$.Rearranging the terms to separate the variables,we get:$y^2 dy = (4 - x^2) dx$.Now,

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

(A) Given the differential equation: $x^2 + y^2 \frac{dy}{dx} = 4$.Rearranging the terms to separate the variables,we get:$y^2 dy = (4 - x^2) dx$.Now,integrate both sides:$\int y^2 dy = \int (4 - x^2) dx$.Performing the integration:$\frac{y^3}{3} = 4x - \frac{x^3}{3} + C_1$.Multiplying the entire equation by $3$:$y^3 = 12x - x^3 + 3C_1$.Let $3C_1 = C$,then:$x^3 + y^3 = 12x + C$.

Class 12 Mathematics Differential Equations Variable separable type differential equations

Difficult

The solution of $x^2 + y^2 \frac{dy}{dx} = 4$ is

AP EAMCET 2001 All AP EAMCET

TS EAMCET 2001 All TS EAMCET

A
$x^3 + y^3 = 12x + C$
B
$x^2 + y^2 = 4x + C$
C
$x^3 - y^3 = 12x + C$
D
$x^2 - y^2 = 4x + C$

Explore More

Browse All

Question Bank

All Subjects

Class 12 Questions

Class 12

Mathematics Questions

Chapter

Differential Equations

Subtopic

Variable separable type differential equations

Previous Year

AP EAMCET 2001 Paper All AP EAMCET years →

Previous Year

TS EAMCET 2001 Paper All TS EAMCET years →

The solution of the differential equation $\frac{dy}{dx} + \frac{1 + x^2}{x} = 0$ is

Easy

View Solution

The particular solution of the differential equation $\frac{dy}{dx} = -4xy^2$ with the initial condition $x = 0, y = 1$ is . . . . . . .

EasyGUJCET 2023

View Solution

The solution of the equation $\frac{dy}{dx} = y(e^x + 1)$ is

Easy

View Solution

The solution of the differential equation $x \, dy + y \, dx - \sqrt{1 - x^2 y^2} \, dx = 0$ is

Difficult

View Solution

The solution of the differential equation $x \frac{dy}{dx} - y = 3$ represents a family of

MediumKCET 2018

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 solution of $x^2 + y^2 \frac{dy}{dx} = 4$ is

Similar Questions

The solution of the differential equation $\frac{dy}{dx} + \frac{1 + x^2}{x} = 0$ is

The particular solution of the differential equation $\frac{dy}{dx} = -4xy^2$ with the initial condition $x = 0, y = 1$ is . . . . . . .

The solution of the equation $\frac{dy}{dx} = y(e^x + 1)$ is

The solution of the differential equation $x \, dy + y \, dx - \sqrt{1 - x^2 y^2} \, dx = 0$ is

The solution of the differential equation $x \frac{dy}{dx} - y = 3$ represents a family of

Vedclass Test Series

Exam Paper Generator

Online Exam Module