Question
In: Advanced Math
Students will be asked to formulate, define, and interpret mathematical modeling (particularly ordinary differential equation) which...
Students will be asked to formulate, define, and interpret mathematical modeling (particularly ordinary differential equation) which involves real engineering applications and related to their majoring (E.g. Newton’s law cooling/warming, mixture problem, radioactive decay, spring-mass system, series circuit, deflection of the beam, etc.).. The selected model should be solved analytically using any methods that have been learnt in the mathematic lecture. just give me an example with related topic and how to solve it using math
Solutions
Colby Messinger answered 1 year agoRelated Solutions
Students will be asked to formulate, define, and interpret mathematical modeling (particularly ordinary differential equation) which...
Students will be asked to formulate, define, and interpret
mathematical modeling (particularly ordinary differential equation)
which involves real engineering applications and related to their
majoring (E.g. Newton’s law cooling/warming, mixture problem,
radioactive decay, spring-mass system, series circuit, deflection
of the beam, etc.).. The selected model should be solved
analytically using any methods that have been learnt in the
mathematic lecture. just give me an example with related topic and
how to solve it using math
Ordinary Differential equation (Newton's Law)
An object is thrown vertically upward from the ground with an initial velocity of 1960 cm/s. neglecting air resistance, find a) the maximum height reached, and b) the total time is taken to return to the starting point.
Series Solutions of Ordinary Differential Equations For the following problems solve the given differential equation by...
Series Solutions of Ordinary Differential Equations For the
following problems solve the given differential equation by means
of a power series about the given point x0. Find the recurrence
relation; also find the first four terms in each of two linearly
independent solutions (unless the series terminates sooner). If
possible, find the general term in each solution.
(1-x)y"+xy-y=0, x0=0
Series Solutions of Ordinary Differential Equations For the following problems solve the given differential equation by...
Series Solutions of Ordinary Differential Equations For the
following problems solve the given differential equation by means
of a power series about the given point x0. Find the recurrence
relation; also find the first four terms in each of two linearly
independent solutions (unless the series terminates sooner). If
possible, find the general term in each solution.
(4-x2)y"+2y=0, x0
1. Give an example of a 3rd order nonlinear ordinary differential equation.
1. Give an example of a 3rd order nonlinear ordinary
differential equation.
The forcing function is a linearly combination of ?(?)=3? and ?(?)=25sin(3?). Solve the Ordinary Differential Equation,...
The forcing function is a linearly combination of ?(?)=3? and
?(?)=25sin(3?).
Solve the Ordinary Differential Equation,
?’’−2?’+?=3?+10sin(3?).
Find two linearly independent power series solutions of the given differential equation about the ordinary point...
Find two linearly independent power series solutions of the
given differential equation about the ordinary point x=0.
y''-2xy=0
Determine the solution of a homogeneous linear first order Ordinary Differential Equation system: (use 2 methods,...
Determine the solution of a homogeneous linear first order
Ordinary Differential Equation system: (use 2 methods, substitution
method, and matrix method)
x1'
= -
4x1-6x2
x2'
=
x1+
x2
With the initial values: x1 (0) = 2 ;
x2 (0) = -1
b. x1'
=
-x2
x2'
=
-x1
With initial values: x1 (0) = 3 ;
x2 (0) = 1
a) Define which differential equations are called linear and which are called nonlinear?
a) Define which differential equations are called linear and which are called nonlinear? [10 marks]
b) Define which systems of differential equations are called homogeneous and which are called non-homogeneous? [10 marks]
c) What is the general structure of solution of a linear nonhomogeneous differential equation? [10 marks]
d) What is the principle of superposition in application to the solution of ordinary differential equations (ODEs)? To which kind of ODEs is it applicable? [10 marks]
Find a recurrence relation fot the power series solutions of differential equation y''-2xy'+8y=0 about the ordinary...
Find a recurrence relation fot the power series solutions of
differential equation y''-2xy'+8y=0 about the ordinary point
x=0.
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