In each of Problems 27 through 43 , solve the given initial value problem. Sketch the graph of its solution and describe its behaviour for increasing t . y ' ' + 4 y ' + 5 y = 0 , y ( 0 ) = 1 , y ' ( 0 ) = 0
In each of Problems 27 through 43 , solve the given initial value problem. Sketch the graph of its solution and describe its behaviour for increasing t . y ' ' + 4 y ' + 5 y = 0 , y ( 0 ) = 1 , y ' ( 0 ) = 0
In each of Problems
27
through
43
, solve the given initial value problem. Sketch the graph of its solution and describe its behaviour for increasing
t
.
y
'
'
+
4
y
'
+
5
y
=
0
,
y
(
0
)
=
1
,
y
'
(
0
)
=
0
Solve the following initial value problem over the interval from t= 0 to 2
where y(0)=1.
dy
yt² - 1.1y
dt
Using Euler's method with h=0.5 and 0.25.
Q5*) Write down an immediate first integral for the Euler-Lagrange equation for the integral
I =
= F(x, y, y″) dx.
Hence write down a first integral of the Euler-Lagrange equation for the integral
I
1 = √(xy ² + x³y²)
dx.
Find the general solution of this ordinary differential equation, seeking first the complementary function and
then the particular integral. (Hint: the ODE is of homogeneous degree. And, for the particular integral, try
functions proportional to log x.)
You are provided with three 2D data points, p1, p2 and p3. Solving A C = B for C provides youwith the coefficients of a natural cubic spline curve that interpolates these points.Additionally, you have been given A and B, but some elements are missing. Moreover, the last two rowsof A are entirely absent. Your task is to determine and fill in the missing elements. For the last two rows,enforce a zero tangent at the beginning (in p1) and a not-a-knot boundary condition in p2. The matricesA and B are given as follows:Explain how to find the entries of A and B . How would you adapt these matrices if the data pointswere 3D? What if your spline should go through five data points? How many “extra rows” would there thenbe (with “extra” meaning “in addition to securing C2-continuity”)?
Chapter 4 Solutions
Differential Equations: An Introduction To Modern Methods And Applications 3e Binder Ready Version + Wileyplus Registration Card
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.
01 - What Is A Differential Equation in Calculus? Learn to Solve Ordinary Differential Equations.; Author: Math and Science;https://www.youtube.com/watch?v=K80YEHQpx9g;License: Standard YouTube License, CC-BY
Higher Order Differential Equation with constant coefficient (GATE) (Part 1) l GATE 2018; Author: GATE Lectures by Dishank;https://www.youtube.com/watch?v=ODxP7BbqAjA;License: Standard YouTube License, CC-BY