The order and degree of differential equation y = px + √(a^2p^2 + b^2), p = dy/dx, a and b are constants are: Option 1: order = 1, degree = 1 Option 2: order = 2, degree = 1/2 Option 3: order = 1, degree not defined Option 4: order = 1, degree = 2

Answer: order = 1, degree = 2. Solution: Write y-px=√(a^2p^2+b^2) and square to remove the radical: (y-px)^2=a^2p^2+b^2. The highest derivative present is p=dy/dx, so the order is 1, and after rationalising, the highest power of p is 2, so the degree is 2.

Calculus

Differential Equations

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The order and degree of differential equation $y = px + \sqrt{a^2p^2 + b^2}, p = \dfrac{dy}{dx}$ , $a$ and $b$ are constants are:

order = 1, degree = 1

order = 2, degree = 1/2

order = 1, degree not defined

order = 1, degree = 2

✅ Correct Option: 4

Write $y-px=\sqrt{a^2p^2+b^2}$ and square to remove the radical: $(y-px)^2=a^2p^2+b^2$ . The highest derivative present is $p=\frac{dy}{dx}$ , so the order is $1$ , and after rationalising, the highest power of $p$ is $2$ , so the degree is $2$ .

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The particular solution of the differential equation $\frac{dy}{dx} = 8yx$ when $y = 1$ at $x = 0$

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Match List-I with List-II

List-I	List-II
Differential Equation	General solution
---	---
(A) $\dfrac{dy}{dx} = \dfrac{y}{x}; x \neq 0$	(I) $y = cx; c \text{ is an arbitrary constant}$
(B) $x dx - y dy = 0; y \neq 0, x \neq 0$	(II) $x^2 - y^2 = c; c \text{ is an arbitrary constant}$
(C) $\dfrac{(x^2 - 1)}{y^2 + 1}\dfrac{dx}{dy} = 1$	(III) $2x + 3y = c; c \text{ is an arbitrary constant}$
(D) $2 dx + 3 dy = 0$	(IV) $(x^3-y^3) = c + 3(x+y); c \text{ is an arbitrary constant}$

Choose the correct answer from the options given below:

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General solution of the differential equation $x(xdy - ydx) = y\,dx$ is :(where c is an arbitrary constant)

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The general solution of the differential equation $x(1 + y^2)dx + y(1 + x^2)dy = 0$ is

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The differential equation of the family of curves $y = a \sin(bx + c)$ , a and c are parameters, is :

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The differential equation whose order and degree are 3 and 2 respectively is

The order and degree of differential equation y=px+a2p2+b2,p=dydxy = px + \sqrt{a^2p^2 + b^2}, p = \dfrac{dy}{dx}y=px+a2p2+b2​,p=dxdy​, aaa and bbb are constants are:

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CUET Mathematics Past Year Questions (Topic-Wise)

The order and degree of differential equation $y = px + \sqrt{a^2p^2 + b^2}, p = \dfrac{dy}{dx}$ , $a$ and $b$ are constants are: