CUET CUET Mathematics 2024 - For the differential equation (x _e x) d y=( _e x-y) d x (A) Degree of the given differential equation is 1. (B) It is a homogeneous differential equation. (C) Solution is 2y _e x+A=( _e x)^2, where A is an arbitrary constant (D) Solution is 2 y _e x+A= _e( _e x), where A is an arbitrary constant Choose the correct answer from the options given below : | PYQs + Solutions

CUET Mathematics 2024

Calculus

Differential Equations

Medium

For the differential equation $\left(x \log _{e} x\right) d y=\left(\log _{e} x-y\right) d x$
(A) Degree of the given differential equation is $1$ .
(B) It is a homogeneous differential equation.
(C) Solution is $2y \log _{\mathrm{e}} \mathrm{x}+A=\left(\log _{\mathrm{e}} \mathrm{x}\right)^{2}$ , where $A$ is an arbitrary constant
(D) Solution is $2 y \log _{e} x+A=\log _{e}\left(\log _{e} x\right)$ , where $A$ is an arbitrary constant
Choose the correct answer from the options given below :

(A) and (C) only

(A), (B) and (C) only

(A), (B) and (D) only

(A) and (D) only

Correct Option: 1

Will be added.

Related questions:

CUET Mathematics 2024

List-I	List-II
(A) Integrating factor of $x \, dy - (y + 2x^2) \, dx = 0$	(I) $\frac{1}{x}$
(B) Integrating factor of $(2x^2 - 3y) \, dx = x \, dy$	(II) $x$
(C) Integrating factor of $(2y + 3x^2) \, dx + x \, dy = 0$	(III) $x^2$
(D) Integrating factor of $2x \, dy + (3x^3 + 2y) \, dx = 0$	(IV) $x^3$

CUET Mathematics 2024

\sin y=x \sin (a+y)

\frac{d y}{d x}

CUET Mathematics 2024

\left(1-\left(\frac{d y}{d x}\right)^{2}\right)^{\frac{3}{2}}=k \frac{d^{2} y}{d x^{2}}