Calculus

Differential Equations

Medium

applied

Let y(x) be the solution curve of the differential equation $x(1+y^2)dx - y(1+x^2)dy = 0$ and it passes through the point (0, 1), then

$y^2=2x^2+1$

$y=(2x+1)^2$

$y=2x^2+3x+1$

$y^2=\log\lvert 1+x \rvert+x^2+1$

✅ Correct Option: 1

Separating, $\frac{x\,dx}{1+x^2}=\frac{y\,dy}{1+y^2}$ .

Integrating gives $\frac12\log(1+x^2)=\frac12\log(1+y^2)+\log k$ , so $1+y^2=c(1+x^2)$ .

At $(0,1)$ : $2=c$ . Hence $y^2=2x^2+1$ .

2025: 22 May Shift 2

The solution of the differential equation $\frac{dy}{dx} = (1 + x^2)(1 + y^2)$ is (Here C is an arbitrary constant)

2023: 22 May Shift 3

Integerating factor of $(x \log_e x) \frac{dy}{dx} + y = 2 \log_e x$ is :

2022: 10 Aug Shift 1

The differential equation representing family of curves $y = ae^{mx} + be^{nx}$ , where $a$ and $b$ are arbitrary constants, is

2022: 23 Aug Shift 1

The integrating factor of the differential equation $x\frac{dy}{dx} - y = 2x^2$ is :

2026: 21 May Shift 1

General solution of the Differential equation $\frac{dy}{dx} + ay = e^{mx}$ is

2026: 19 May Shift 2

Which of the following statements are TRUE?

A. Order of the differential equation is the order of highest differential appearing in the differential equation.

B. Degree of a differential equation is a real number.

C. Order of a differential equation is whole number.

D. Degree of a differential equation is the degree of the highest order derivative, when differential coefficients are free from radicals and fractions.

Choose the correct answer from the options given below:

Let y(x) be the solution curve of the differential equation x(1+y2)dx−y(1+x2)dy=0x(1+y^2)dx - y(1+x^2)dy = 0x(1+y2)dx−y(1+x2)dy=0 and it passes through the point (0, 1), then

Solution

Related questions:

Keyboard Shortcuts

CUET Mathematics Past Year Questions (Topic-Wise)

Let y(x) be the solution curve of the differential equation $x(1+y^2)dx - y(1+x^2)dy = 0$ and it passes through the point (0, 1), then