The solution of the differentiable equation 2xdy/dx + y = 14x^3, x > 0, is Option 1: y = 2x^3 + c x^(1/2) Option 2: y = x^3 + c x^(1/2) Option 3: y = 2x^3 + c x^(-1/2) Option 4: y = x^3 + c x^(-1/2)

Answer: y = 2x^3 + c x^(-1/2). Solution: Standard form: dy/dx + y/2x = 7x^2. Integrating factor = e^( 1/2xdx) = √x. So y√x = 7x^(5/2) dx = 2x^(7/2) + c. Therefore y = 2x^3 + cx^(-1/2).

Calculus

Differential Equations

Medium

core

The solution of the differentiable equation $2x\frac{dy}{dx} + y = 14x^3, x > 0$ , is

$y = 2x^3 + c x^{\frac{1}{2}}$

$y = x^3 + c x^{\frac{1}{2}}$

$y = 2x^3 + c x^{-\frac{1}{2}}$

$y = x^3 + c x^{-\frac{1}{2}}$

✅ Correct Option: 3

Standard form: $\frac{dy}{dx} + \frac{y}{2x} = 7x^2$ . Integrating factor $= e^{\int \frac{1}{2x}dx} = \sqrt{x}$ . So $y\sqrt{x} = \int 7x^{5/2}\,dx = 2x^{7/2} + c$ . Therefore $y = 2x^3 + cx^{-1/2}$ .

2023: 30 May Shift 3

If m and n are respectively the order and degree of the differential equation :

$\left(\frac{d^2 y}{dx^2}\right)^5 + 6 \frac{\left(\frac{d^2 y}{dx^2}\right)^3}{\frac{d^3 y}{dx^3}} + \frac{d^3 y}{dx^3} = x^2 + 5$ , then :

2026: 26 May Shift 2

If $\dfrac{dy}{dx} = e^{x-y} + x^2e^{-y}$ , then the solution of the differential equation will be:-

2026: 21 May Shift 2

Match the LIST-I with LIST-II

LIST-I (Differential Equation)		LIST-II (Degree of Differential Equation)
A. $\dfrac{d^3y}{dx^3} + \left(\dfrac{d^2y}{dx^2}\right)^2 - \dfrac{dy}{dx} + y = 0$		I. 2
B. $\dfrac{dy}{dx} + \left(\dfrac{d^2y}{dx^2}\right)^4 + 2\left(\dfrac{d^3y}{dx^3}\right)^3 = 0$		II. 4
C. $\left(\dfrac{d^3y}{dx^3}\right)^2 + \left(\dfrac{d^2y}{dx^2}\right)^4 - y = 0$		III. 1
D. $\left(\dfrac{d^2y}{dx^2}\right)^4 + \left(\dfrac{dy}{dx}\right)^3 + y = 0$		IV. 3

Choose the correct answer from the options given below:

2026: 31 May Shift 2

Match the LIST-I with LIST-II

	LIST-I Differential equation		LIST-II Integrating factor
A.	$\dfrac{dy}{dx} + 3y = e^{-2x}$	I.	$\dfrac{1}{x}$
B.	$x\dfrac{dy}{dx} + y = 3x^2$	II.	$e^{-x}$
C.	$x\dfrac{dy}{dx} - y = 3x^2$	III.	$x$
D.	$\dfrac{dy}{dx} - y = x$	IV.	$e^{3x}$

Choose the correct answer from the options given below:

2025: 15 May Shift 2

Match List-I with List-II

List-I	List-II
Differential equation	Order and degree
(A) $(y'')^3 + (y')^4 - 6 = (y''')^2$	(I) Order = 1, Degree = 2
(B) $\sqrt{(y')^2 + 5} = y''$	(II) Order = 2, Degree = 3
(C) $(y')^2 = (2 + y'')^{3/2}$	(III) Order = 2, Degree = 2
(D) $y = xy' + \sqrt{a^2(y')^2 + b^2}$	(IV) Order = 3, Degree = 2

Choose the correct answer from the options given below:

2025: 3 June Shift 2

The sum of the order and degree of the differential equation representing the family of curves $y = mx + m^4$ , where m is arbitrary constant, is

The solution of the differentiable equation 2xdydx+y=14x3,x>02x\frac{dy}{dx} + y = 14x^3, x > 02xdxdy​+y=14x3,x>0, is

Solution

Related questions:

Keyboard Shortcuts

CUET Mathematics Past Year Questions (Topic-Wise)

The solution of the differentiable equation $2x\frac{dy}{dx} + y = 14x^3, x > 0$ , is