Gujarat Technological UniversityWinter 2025 examination

GTU 3110015 Mathematics - 2 (Maths 2) Winter 2025 Question Paper & PDF

B.E. · Common Engineering · Semesters 1 and 2 · Subject code 3110015
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Total
70 marks
To pass
23 marks (33%)
Duration
2.5 Hours 2:30 PM – 5:30 PM
Questions
5 with internal choice
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3 of 25 questions on this paper were also asked in other years. 20 more are types of question GTU sets again with new data. Each is marked below with the years it appeared.See all 27 repeated 3110015 questions, most asked first

Q.1

14 Marks
(a)
3 marks
If ϕ\phi is a scalar field, prove that curl(grad ϕ)=0\text{curl}(\text{grad } \phi) = 0.
(b)
4 marksSame type asked in 4 of 6 papers
Determine whether the vector field u⃗=y2i^+2xyj^−z2k^\vec{u} = y^2 \hat{i} + 2xy \hat{j} - z^2 \hat{k} is solenoidal or irrotational at the point (1,2,1)(1, 2, 1)?

Also asked in Summer 2025 Q1a, Winter 2023 Q1b, Summer 2023 Q1b

(c)
7 marksSame type asked in 6 of 6 papers
Verify Green’s theorem in the plane for F⃗=(x2+y2)i^−2xyj^\vec{F} = (x^2 + y^2)\hat{i} - 2xy\hat{j} taken around the rectangle bounded by the lines x=±1,y=0x = \pm 1, y = 0 and y=2y = 2.

Also asked in Summer 2025 Q1c, Winter 2024 Q1c, Summer 2024 Q1c, Winter 2023 Q1c, Summer 2023 Q1c

Q.2

14 Marks
(a)
3 marks
Define order and degree of the ordinary differential equation. Give an example of ordinary differential equation:
ifirst order first degree, (ii) first order higher degree.
(b)
4 marksSame type asked in 6 of 6 papers
Find the Laplace transform of:
itcos⁡2tt \cos^2 t
iisin⁡tt\frac{\sin t}{t}

Also asked in Summer 2025 Q4a, Summer 2025 Q4b, Summer 2025 Q4b OR, Winter 2024 Q2a, Winter 2024 Q3b, Winter 2024 Q4b OR, Winter 2024 Q5a OR, Summer 2024 Q2a, Summer 2024 Q3b OR, Summer 2024 Q4a OR, Winter 2023 Q2b, Summer 2023 Q3a, Summer 2023 Q3a OR

(c)
7 marksAsked in 2 of 6 papers
Apply the method of undetermined coefficients to solve the differential equation
(D2−2D+5)y=5x3−6x2+6x(D^2 - 2D + 5)y = 5x^3 - 6x^2 + 6x

Also asked in Summer 2024 Q4c OR

(c)
7 marksSame type asked in 6 of 6 papers
Apply the variation of parameters method to solve the differential equation
(D2−3D+2)y=ex(D^2 - 3D + 2)y = e^x

Also asked in Summer 2025 Q5c, Winter 2024 Q4c, Summer 2024 Q4c, Winter 2023 Q4c OR, Summer 2023 Q5c OR

Q.3

14 Marks
(a)
3 marksSame type asked in 6 of 6 papers
State first shifting theorem for Laplace transform. Find the Laplace transform of e−3t(t2+sin⁡t)e^{-3t}(t^2 + \sin t).

Also asked in Summer 2025 Q4a, Summer 2025 Q4b, Summer 2025 Q4b OR, Winter 2024 Q2a, Winter 2024 Q3b, Winter 2024 Q4b OR, Winter 2024 Q5a OR, Summer 2024 Q2a, Summer 2024 Q3b OR, Summer 2024 Q4a OR, Winter 2023 Q2b, Summer 2023 Q3a, Summer 2023 Q3a OR

(b)
4 marksSame type asked in 4 of 6 papers
Find the general solution of the differential equation x2y dx−(x3+xy2) dy=0x^2 y \, dx - (x^3 + xy^2) \, dy = 0.

Also asked in Summer 2025 Q5a OR, Summer 2024 Q3a OR, Summer 2023 Q4a, Summer 2023 Q4a OR

(c)
7 marksSame type asked in 6 of 6 papers
Apply Laplace transform to solve the initial value problem:

y′′−6y′+9y=t2e3t,y(0)=2,  y′(0)=6y'' - 6y' + 9y = t^2 e^{3t}, \quad y(0) = 2, \; y'(0) = 6

Also asked in Summer 2025 Q4c, Winter 2024 Q3c OR, Summer 2024 Q2c OR, Winter 2023 Q2c, Summer 2023 Q3c

(a)
3 marksSame type asked in 6 of 6 papers
State convolution theorem for Laplace transform. Find the inverse Laplace transform of
1s(s+1)\frac{1}{s(s+1)}

Also asked in Summer 2025 Q4a OR, Summer 2025 Q4c OR, Winter 2024 Q3a OR, Winter 2024 Q3c, Winter 2024 Q4a, Summer 2024 Q2c, Summer 2024 Q3b, Winter 2023 Q2a, Summer 2023 Q3b, Summer 2023 Q3b OR

(b)
4 marksSame type asked in 4 of 6 papers
Check whether the given differential equation is exact or not:

(x4−2xy2+y4) dx−(2x2y−4xy3+sin⁡y) dy=0(x^4 - 2xy^2 + y^4) \, dx - (2x^2 y - 4xy^3 + \sin y) \, dy = 0

Also asked in Summer 2025 Q5a OR, Summer 2024 Q3a OR, Summer 2023 Q4a, Summer 2023 Q4a OR

(c)
7 marksSame type asked in 4 of 6 papers
Find the Fourier cosine integral representation of
f(x)=π2e−x,x>0f(x) = \frac{\pi}{2} e^{-x}, \quad x > 0

Also asked in Summer 2025 Q1b, Summer 2024 Q2b, Summer 2023 Q3c OR

Q.4

14 Marks
(a)
3 marksSame type asked in 5 of 6 papers
Find the general solution of the differential equation: y′+2ytan⁡x=sin⁡xy' + 2y \tan x = \sin x.

Also asked in Summer 2025 Q5a, Summer 2025 Q5b OR, Winter 2024 Q5a, Winter 2023 Q3a, Winter 2023 Q3a OR, Summer 2023 Q4c

(b)
4 marksSame type asked in 5 of 6 papers
Solve the Euler-Cauchy differential equation: (4x2D2+16xD+9)y=0(4x^2 D^2 + 16xD + 9)y = 0.

Also asked in Summer 2025 Q3c OR, Winter 2024 Q5b OR, Summer 2024 Q5a, Winter 2023 Q4b

(c)
7 marksSame type asked in 6 of 6 papers
Solve:
i(D2−4)y=e2x+e−4x(D^2 - 4)y = e^{2x} + e^{-4x}
ii(D3−3D2−D+3)y=1(D^3 - 3D^2 - D + 3)y = 1

Also asked in Summer 2025 Q3a, Summer 2025 Q3b, Summer 2025 Q3a OR, Summer 2025 Q3b OR, Summer 2025 Q5c OR, Winter 2024 Q4b, Summer 2024 Q3a, Summer 2024 Q4b OR, Summer 2024 Q5b, Winter 2023 Q3b, Winter 2023 Q4a, Winter 2023 Q4a OR, Winter 2023 Q4b OR, Summer 2023 Q4b, Summer 2023 Q4b OR, Summer 2023 Q5a, Summer 2023 Q5a OR, Summer 2023 Q5c

(a)
3 marksSame type asked in 6 of 6 papers
Solve: x2p2+xyp−6y2=0x^2 p^2 + xyp - 6y^2 = 0.

Also asked in Summer 2025 Q5b, Winter 2024 Q3b OR, Summer 2024 Q3c, Winter 2023 Q3c, Winter 2023 Q3c OR, Summer 2023 Q4c OR

(b)
4 marksAsked in 2 of 6 papers
If y1=xy_1 = x is one solution of x2y′′+xy′−y=0x^2 y'' + xy' - y = 0, find the second solution.

Also asked in Summer 2024 Q4b

(c)
7 marksSame type asked in 6 of 6 papers
Solve:
i(D2+9)y=cos⁡4x(D^2 + 9)y = \cos 4x
ii(D3−5D2+8D−4)y=e−x(D^3 - 5D^2 + 8D - 4)y = e^{-x}

Also asked in Summer 2025 Q3a, Summer 2025 Q3b, Summer 2025 Q3a OR, Summer 2025 Q3b OR, Summer 2025 Q5c OR, Winter 2024 Q4b, Summer 2024 Q3a, Summer 2024 Q4b OR, Summer 2024 Q5b, Winter 2023 Q3b, Winter 2023 Q4a, Winter 2023 Q4a OR, Winter 2023 Q4b OR, Summer 2023 Q4b, Summer 2023 Q4b OR, Summer 2023 Q5a, Summer 2023 Q5a OR, Summer 2023 Q5c

Q.5

14 Marks
(a)
3 marksSame type asked in 3 of 6 papers
Classify the singular points of the differential equation x2y′′+xy′−2y=0x^2 y'' + xy' - 2y = 0.

Also asked in Winter 2023 Q5a, Winter 2023 Q5a OR, Summer 2023 Q2a

(b)
4 marksSame type asked in 6 of 6 papers
Find the series solution of y′′=2y′y'' = 2y' in powers of xx.

Also asked in Summer 2025 Q2c, Winter 2024 Q2c, Summer 2024 Q5c, Winter 2023 Q5b, Winter 2023 Q5c, Winter 2023 Q5b OR, Summer 2023 Q2c

(c)
7 marksAsked in 2 of 6 papers
Using the power-series method, solve (1−x2)y′′−2xy′+2y=0(1 - x^2)y'' - 2xy' + 2y = 0.

Also asked in Summer 2025 Q2c OR

(a)
3 marksSame type asked in 3 of 6 papers
Discuss about ordinary point, singular point, regular singular point and irregular singular point for the differential equation
x3(x−1)y′′+3(x−1)y′+7xy=0x^3 (x - 1)y'' + 3(x - 1)y' + 7xy = 0

Also asked in Winter 2023 Q5a, Winter 2023 Q5a OR, Summer 2023 Q2a

(b)
4 marksSame type asked in 3 of 6 papers
Derive recurrence relation for the Bessel’s polynomial Jn(x)J_n(x).

Also asked in Winter 2024 Q5c, Winter 2024 Q5c OR, Summer 2024 Q5b OR

(c)
7 marksSame type asked in 6 of 6 papers
Find the series solution of 2x(x−1)y′′−(x+1)y′+y=02x(x - 1)y'' - (x + 1)y' + y = 0 at x=0x = 0.

Also asked in Summer 2025 Q2c, Winter 2024 Q2c, Summer 2024 Q5c, Winter 2023 Q5b, Winter 2023 Q5c, Winter 2023 Q5b OR, Summer 2023 Q2c

More Mathematics - 2 papers

Questions repeat across sessions. Working through two or three papers shows you which topics GTU asks most.

Summer 202570 marks · 5 questions
Winter 202470 marks · 5 questions
Summer 202470 marks · 5 questions
Winter 202370 marks · 5 questions

Other Semester 1 subjects

BE Common

3110001
Chemistry
3110002
English
3110003
Programming for Problem Solving
3110004
Basic Civil Engineering

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About this paper

Official Gujarat Technological University (GTU) examination paper for Mathematics - 2 (Maths 2) (Winter 2025, B.E. · Common Engineering, Sem 1). Features complete 70-mark regular & remedial examination pattern, official marking distribution across all 5 questions, and direct 1-click official PDF download.

Transcribed for student exam preparation from Gujarat Technological University official examination archives. Questions, syllabus guidelines, and curriculum marking schemes remain the intellectual property of Gujarat Technological University.

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