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Gujarat Technological UniversityWinter 2025 Examination

GTU 130001 Mathematics-III (Maths 3) Winter 2025 Paper Solution & PDF

B.E. · Computer Engineering · Semester 3 · Subject Code: 130001
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Total Marks70 MarksExternal theory exam
Passing Marks23 Marks33% minimum cutoff
Exam Duration2.5 Hours10:30 AM – 1:30PM
Paper Structure5 QuestionsWith internal OR choices
Jump toQ1Q2Q3Q4Q5

Question 1

14 MarksMedium
(a)
Compute β(92,72)\beta\left(\frac{9}{2}, \frac{7}{2}\right).
7 Marks
(b)
Find the series solution of y′−2xy=0y' - 2xy = 0.
7 Marks

Question 2

14 MarksMedium
(a)
Solve y′′+y′−12y=e6xy'' + y' - 12y = e^{6x}.
7 Marks
(b)
Test the exactness and solve (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.
7 Marks
OR OPTION
(b)
Solve dydx+ysin⁡x=ecos⁡x\frac{dy}{dx} + y\sin x = e^{\cos x}.
7 Marks

Question 3

14 MarksMedium
(a)
Solve y′′+y=sin⁡xy'' + y = \sin x by using method of variation of parameters.
7 Marks
(b)
Find the half range sine series of f(x)=x2f(x) = x^2 in the interval (0,π)(0, \pi).
7 Marks
OR OPTION
(a)
Solve x2y′′−20y=0x^2 y'' - 20y = 0.
7 Marks
(b)
Find the Fourier series of f(x)=xf(x) = x in the interval (0,2π)(0, 2\pi).
7 Marks

Question 4

14 MarksMedium
(a)
Find L{tcos⁡at}\mathcal{L}\{t \cos at\}.
7 Marks
(b)
Find L−1{s+2s(s+1)(s+3)}\mathcal{L}^{-1}\left\{\frac{s+2}{s(s+1)(s+3)}\right\}.
7 Marks
OR OPTION
(a)
Find L{∫0te−2tt3 dt}\mathcal{L}\left\{\int_0^t e^{-2t} t^3 \, dt\right\}.
7 Marks
(b)
Solve dydt+2y=e−3t\frac{dy}{dt} + 2y = e^{-3t}, y(0)=1y(0) = 1 by using Laplace transform.
7 Marks

Question 5

14 MarksMedium
(a)
Solve xp+yq=3zxp + yq = 3z.
7 Marks
(b)
Solve p2+q2=x2+y2p^2 + q^2 = x^2 + y^2.
7 Marks
OR OPTION
(a)
Solve ∂2z∂x2−2∂2z∂x∂y+∂2z∂y2=ex+4y\frac{\partial^2 z}{\partial x^2} - 2\frac{\partial^2 z}{\partial x \partial y} + \frac{\partial^2 z}{\partial y^2} = e^{x+4y}.
7 Marks
(b)
Using the method of separation of variables, solve ∂u∂x=2∂u∂t+u\frac{\partial u}{\partial x} = 2\frac{\partial u}{\partial t} + u given that u(x,0)=6e−3xu(x, 0) = 6e^{-3x}.
7 Marks
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About this Examination Paper & Attribution

Official Gujarat Technological University (GTU) examination paper and step-by-step solutions for Mathematics-III (Maths 3) (Winter 2025, B.E. · Computer Engineering, Sem 3). 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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