The solution of the differential equation dy/dx = 6/x^2; y(1) = 3 is : Option 1: y = 9 + 6/x Option 2: y = 9 - 6/x Option 3: y = -9 + 6/x Option 4: y = -3 - 6/x

Answer: y = 9 - 6/x. Solution: Integrate both sides: y = -6/x + C. Using y(1) = 3: 3 = -6 + C C = 9. So y = 9 - 6/x.

Calculus

Differential Equations

Easy

common

The solution of the differential equation $\frac{dy}{dx} = \frac{6}{x^2}$ ; $y(1) = 3$ is :

$y = 9 + \frac{6}{x}$

$y = 9 - \frac{6}{x}$

$y = -9 + \frac{6}{x}$

$y = -3 - \frac{6}{x}$

✅ Correct Option: 2

Integrate both sides: $y = -\frac{6}{x} + C$ .

Using $y(1) = 3$ : $3 = -6 + C \Rightarrow C = 9$ .

So $y = 9 - \frac{6}{x}$ .

2025: 15 May Shift 1

Consider the differential equation $\frac{dy}{dx} + y \tan x = \sec x$ , then which of the following statements are correct?

(A) It is homogeneous

(B) It has $\sec x$ as its integrating factor

(D) It's degree is not defined

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2026: 14 May Shift 2

The general solution of the differintial equation : $x\frac{dy}{dx}-ay=1(a\neq0)$ is

2022: 7 Aug Shift 2

If $U(x) = x + \sqrt{1 + x^2}$ , then solution of the differential equation $\frac{dy}{dx} + \sqrt{\frac{1 + y^2}{1 + x^2}} = 0$ , is :

2022: 16 July Shift 2

Match List I with List II.

List I	List II
A. $\frac{d^2y}{dx^2} + \frac{dy}{dx} = 0$	I. order 3, degree 1
B. $\left(\frac{d^2y}{dx^2}\right)^2 = 0$	II. order 2, degree 2
C. $\frac{d^3y}{dx^3} + \frac{d^2y}{dx^2} + y = 0$	III. order 2, degree 1
D. $\sin\left(\frac{dy}{dx}\right) + 5y = 0$	IV. order 1, degree is not defined

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2025: 13 May Shift 1

Match List-I with List-II

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2026: 18 May Shift 1

Match List-I with List-II

List-I Differential equation	List-II Curve satisfying the differential equation
(A) $\frac{d^2y}{dx^2}+y=0$	(I) $x^2+y^2=C$ : Where C is an arbitrary constant
(B) $\frac{dy}{dx}+y=\frac{x^2+y}{x}$	(II) $3e^{-4y}+4e^{3x}=C$ : Where C is an arbitrary constant
(C) $\frac{dy}{dx}+\frac{x}{y}=0$	(III) $y=\sin x+\cos x+C$ : Where C is an arbitrary constant
(D) $\log(dy/dx)=3x+4y$	(IV) $y=x+Cxe^{-x}$ : Where C is an arbitrary constant

Choose the correct answer from the options given below: