What is a solution to a differential equation? We said that a differential equation is an equation that
describes the derivative, or derivatives, of a function that is unknown to us. By a solution to a differential
equation, we mean simply a function that satisfies this description.
2. Here is a differential equation which describes an unknown position function s(t):
ds
dt
318
4t+1,
ds
(a) To check that s(t) = 2t2 + t is a solution to this differential equation, calculate
you really do get 4t +1.
and check that
dt'
(b) Is s(t) = 2t2 +++ 4 also a solution to this differential equation?
(c) Is s(t)=2t2 + 3t also a solution to this differential equation?
ds
1
dt
(d) To find all possible solutions, start with the differential equation = 4t + 1, then move dt to the
right side of the equation by multiplying, and then integrate both sides. What do you get?
(e) Does this differential equation have a unique solution, or an infinite family of solutions?
Ministry of Higher Education &
Scientific Research
Babylon University
College of Engineering -
Al musayab
Automobile Department
Subject :Engineering Analysis
Time: 2 hour
Date:27-11-2022
کورس اول تحليلات
تعمیر )
1st month exam / 1st semester (2022-2023)/11/27
Note: Answer all questions,all questions have same degree.
Q1/: Find the following for three only.
1-
4s
C-1
(+2-3)2 (219) 3.0 (6+1)) (+3+5)
(82+28-3),2-
,3-
2-1
4-
Q2/:Determine the Laplace transform of the function t sint.
Q3/: Find the Laplace transform of
1,
0≤t<2,
-2t+1,
2≤t<3,
f(t) =
3t,
t-1,
3≤t 5,
t≥ 5
Q4: Find the Fourier series corresponding to the function
0
-5
Ministry of Higher Education &
Scientific Research
Babylon University
College of Engineering -
Al musayab
Subject :Engineering Analysis
Time: 80 min
Date:11-12-2022
Automobile Department
2nd month exam / 1" semester (2022-2023)
Note: Answer all questions,all questions have same degree.
کورس اول
شعر 3
Q1/: Use a Power series to solve the differential equation:
y" - xy = 0
Q2/:Evaluate using Cauchy's residue theorem,
sinnz²+cosz²
dz, where C is z = 3
(z-1)(z-2)
Q3/:Evaluate
dz
(z²+4)2
Where C is the circle /z-i/-2,using Cauchy's residue theorem.
Examiner: Dr. Wisam N. Hassan
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY