AfterBoards Logo
Skip to main contentSkip to solution

CUET Mathematics 2026 PYQs22 May Shift 1. Free, no login required.

Calculus

past year questions, CUET Mathematics 2026 22 May Shift 1

Differential Equations

past year questions, Calculus, CUET Mathematics 2026 22 May Shift 1

Medium

applied

The particular solution of the differential equation log⁡(dydx)=3x+4y\log\left(\frac{dy}{dx}\right)=3x+4y, given that y=0y=0, when x=0x=0 is:

Solution

✅ Correct Option: 3

The equation is dydx=e3xe4y\frac{dy}{dx}=e^{3x}e^{4y}, so e−4ydy=e3xdxe^{-4y}dy=e^{3x}dx and −e−4y4=e3x3+C-\frac{e^{-4y}}{4}=\frac{e^{3x}}{3}+C.

At (0,0)(0,0), C=−712C=-\frac{7}{12}. Multiplying through by −12-12 gives 4e3x+3e−4y=74e^{3x}+3e^{-4y}=7.

Related questions:

2026: 19 May Shift 1

The general solution of the differential equation dydx+ycot⁡x=2cos⁡x\frac{dy}{dx} + y\cot x = 2\cos x is (Where C is an arbitrary constant)

2023: 22 May Shift 3

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

2025: 13 May Shift 1

The general solution of the differential equation log⁡e(dydx)=ax+by\log_e\left(\frac{dy}{dx}\right) = ax + by is

2026: 19 May Shift 1

The solution of the initial value problem xdydx=2,y(1)=2x\frac{dy}{dx} = 2, y(1) = 2 is

2025: 19 May Shift 1

Match List-I with List-II

List-IList-II
Differential EquationOrder and degree of differential equation
(A) d2ydx2+2(dydx)2=edydx+1\frac{d^2y}{dx^2} + 2\left(\frac{dy}{dx}\right)^2 = e^{\frac{dy}{dx}} + 1(I) Order = 1, Degree = 2
(B) (d2ydx2)2+4(dydx)3=ey−1\left(\frac{d^2y}{dx^2}\right)^2 + 4\left(\frac{dy}{dx}\right)^3 = e^y - 1(II) Order = 2, Degree = 1
(C) 3(dydx)+4y+ey=dxdy3\left(\frac{dy}{dx}\right) + 4y + e^y = \frac{dx}{dy}(III) Order = 2, Degree = 2
(D) d2ydx2+3(dydx)=(ey+dydx)2\frac{d^2y}{dx^2} + 3\left(\frac{dy}{dx}\right) = \left(e^y + \frac{dy}{dx}\right)^2(IV) Order = 2, Degree = Not defined

Choose the correct answer from the options given below:

2025: 21 May Shift 2

Match List-I with List-II

List-IList-II
(A) Integrating factor of xdy−(y+x2)dx=0xdy - (y + x^2)dx = 0(I) x2x^2
(B) Integrating factor of xdy+(2y+x2)dx=0xdy + (2y + x^2)dx = 0(II) x3x^3
(C) Integrating factor of (3y−x2)dx+xdy=0(3y - x^2)dx + xdy = 0(III) xx
(D) Integrating factor of (y+3x2)dx+xdy=0(y + 3x^2)dx + xdy = 0(IV) 1x\frac{1}{x}

Choose the correct answer from the options given below:

Keyboard Shortcuts

  • Left arrow: Previous question
  • Right arrow: Next question
  • S key: Jump to solution
  • Q key: Jump to question

CUET Mathematics Past Year Questions (Topic-Wise)