If m and n are the order and degree of the differential equation 9d^3y/dx^3 = \1 + (dy/dx)^2\^(5/2), then the value of 2m+3n is equal to Option 1: 10 Option 2: 12 Option 3: 15 Option 4: 7

Answer: 12. Solution: Squaring both sides clears the fractional power, giving 81(d^3y/dx^3)^2=\1+(dy/dx)^2\^5. So the order is m=3 and the degree is n=2, making 2m+3n=6+6=12.

Calculus

Differential Equations

Medium

applied

If m and n are the order and degree of the differential equation $9\frac{d^3y}{dx^3} = \left\{1 + \left(\frac{dy}{dx}\right)^2\right\}^{5/2}$ , then the value of $2m+3n$ is equal to

✅ Correct Option: 2

Squaring both sides clears the fractional power, giving $81\left(\frac{d^3y}{dx^3}\right)^2=\left\{1+\left(\frac{dy}{dx}\right)^2\right\}^5$ . So the order is $m=3$ and the degree is $n=2$ , making $2m+3n=6+6=12$ .

2026: 14 May Shift 2

Match the LIST-I with LIST-II

	LIST-I (Differential Equation)		LIST-II (Order and degree)
A.	$\log\left(\dfrac{dy}{dx}\right) + \dfrac{d^2y}{dx^2} = 0$	I.	Order : 3 and degree : not defined
B.	$\dfrac{d^3y}{dx^3} + y^2 + e^{\frac{dy}{dx}} = 4$	II.	Order : 2 and degree : 2
C.	$\dfrac{d}{dx}\left(\dfrac{dy}{dx}\right)^2 + \dfrac{dy}{dx} = \sqrt{x}$	III.	Order : 2 and degree : not defined
D.	$\left(1+\left(\dfrac{dy}{dx}\right)^2\right)^{3/2} = \dfrac{d^2y}{dx^2}$	IV.	Order : 2 and degree : 1

Choose the correct answer from the options given below:

2023: 30 May Shift 3

Solution of differential equation $x dy - y dx = 0$ respresents :

2023: 15 June Shift 2

The differential equation whose solution is $Ax^2 + By^2 = 1$ where A and B are arbitrary constant is of :

(A) first order and first degree

(B) second order and first degree

(D) second order

Choose the correct answer from the options given below :

2025: 30 May Shift 1

For the differential equation $ydx - (x + 3y^2)dy = 0$ , which of the following statements are true?

(A) It is a linear differential equation

(B) It is a homogenous differential equation

(D) If $y(0) = 1$ , then its particular solution is $x = 3y^2 - 1$

Choose the correct answer from the options given below:

2022: 25 May Shift 1

Solution of $\frac{dy}{dx} = (1+x^2)(1+y^2)$ is:

2026: 22 May Shift 2

Match List-I with List-II

List-I: Linear differential equation	List-II: Integrating factor
(A) $x\frac{dy}{dx}-y=2x^3$	(I) $e^{-x}$
(B) $2x\frac{dy}{dx}+y=3x^2$	(II) $e^x$
(C) $\frac{dy}{dx}+y=\cos x-\sin x$	(III) $x^{1/2}$
(D) $\frac{dy}{dx}-y=e^x$	(IV) $1/x$

Choose the correct answer from the options given below:

If m and n are the order and degree of the differential equation 9d3ydx3={1+(dydx)2}5/29\frac{d^3y}{dx^3} = \left\{1 + \left(\frac{dy}{dx}\right)^2\right\}^{5/2}9dx3d3y​={1+(dxdy​)2}5/2, then the value of 2m+3n2m+3n2m+3n is equal to

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

If m and n are the order and degree of the differential equation $9\frac{d^3y}{dx^3} = \left\{1 + \left(\frac{dy}{dx}\right)^2\right\}^{5/2}$ , then the value of $2m+3n$ is equal to