Match List-I with List-II, List-I, List-II, (A) The degree of differential equation d^3y/dx^3 = e^(dx/dy), (I) 2, (B) The order of differential equation (dy/dx)^2 + d^3y/dx^3 = 0, (II) 4, (C) The sum of order and degree of differential equation d/dx(d^2y/dx^2) + (dy/dx)^5 = x, (III) not defined, (D) The number of arbitrary constants in the general solution of a differential equation of order 2, (IV) 3, Choose the correct answer from the options given below:

Question

Match List-I with List-II | List-I | List-II | |---|---| | (A) The degree of differential equation $$\frac{d^3y}{dx^3} = e^{\frac{dx}{dy}}$$ | (I) 2 | | (B) The order of differential equation $$\left(\frac{dy}{dx}\right)^2 + \frac{d^3y}{dx^3} = 0$$ | (II) 4 | | (C) The sum of order and degree of differential equation $$\frac{d}{dx}\left(\frac{d^2y}{dx^2}\right) + \left(\frac{dy}{dx}\right)^5 = x$$ | (III) not defined | | (D) The number of arbitrary constants in the general solution of a differential equation of order 2 | (IV) 3 | Choose the correct answer from the options given below:

Accepted Answer

(A) - (III), (B) - (IV), (C) - (II), (D) - (I)

Answer

(A) - (I), (B) - (IV), (C) - (II), (D) - (III)

Answer

(A) - (II), (B) - (I), (C) - (III), (D) - (IV)

Answer

(A) - (IV), (B) - (I), (C) - (II), (D) - (III)

List-I	List-II
(A) $y + \frac{dy}{dx} = \frac{1}{4}\int y\,dx$	(I) Order 1, Degree 1
(B) $y = \frac{dy}{dx} + \frac{C}{dy/dx}$	(II) Order 2, Degree 2
(C) $(xy^2+x)dx + (y-x^2)dy = 0$	(III) Order 2, Degree 1
(D) $\left[\left\{1+\left(\frac{dy}{dx}\right)^2\right\}^{3/2}/\frac{d^2y}{dx^2}\right] = K$	(IV) Order 1, Degree 2

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

List-I	List-II
(A) The degree of differential equation $\frac{d^3y}{dx^3} = e^{\frac{dx}{dy}}$	(I) 2
(B) The order of differential equation $\left(\frac{dy}{dx}\right)^2 + \frac{d^3y}{dx^3} = 0$	(II) 4
(C) The sum of order and degree of differential equation $\frac{d}{dx}\left(\frac{d^2y}{dx^2}\right) + \left(\frac{dy}{dx}\right)^5 = x$	(III) not defined
(D) The number of arbitrary constants in the general solution of a differential equation of order 2	(IV) 3

Solution

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