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 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. Use Laplace transforms to solve the following differential
equations for ?(?) for ? ≥ 0. Use ?(0) = 0 and ?̇(0) = 1 for each
case.
i. 0 = ?̈(?) + 2?̇(?) + 4?(?)
ii. 0 = ?̈(?) + 3?̇(?) + 2?(?)
iii. 5 = ?̈(?) + 5?̇(?) + 6?(?)
3. For the three differential equations from problem one
determine the steady-state value of the system using:
a. lim?→0 ??(?),
b. lim ?→∞ ?(?) analytically,
c. lim ?→∞ ?(?)...
Solve the following problems.
a) What is the order of the differential equation ? ′ = ? 2 − 3?
− 10? Is it linear ?
b) Determine whether the differential equation ? ′ = ? 2 − 3? −
10 possesses constant solutions. If yes find these constant
solutions.
c) Find the value(s) of ? so that the function ? = ? ?? is a
solution of ? ′′ − 3? ′ − 10? = 0.
Do you think...
2- Ordinary Differential Equations
a) y'+y = sen(x)
b)By what technique do you solve an ODE below: (x + yˆ2) dy +
(y-xˆ2) dx = 0?
c) Solve the following ODE by Exact Equation: y '= 2x
d) Resolution y '= (2 + exp (xy)) / (2y-xexp (xy))
How can we use algebraic skills and properties to conduct
business and solve business problems? What is an example of a way
we can use algebraic skills to make decisions?
Use the Laplace transform to solve the given system of
differential equations. d2x dt2 + 3 dy dt + 3y = 0 d2x dt2 + 3y =
te−t x(0) = 0, x'(0) = 4, y(0) = 0