OEF ODE
--- Introduction ---
This module actually contains 16 exercises on (elementary) ordinary
differential equations.
Coefficients order 2 I
The differential equation
.
has
as a solution. What are the values of
and
?
Give the exact values of the constants.
Coefficients order 2 II
The differential equation
has
as a solution. What are the values of
and
?
Give the exact values of the constants.
Coefficients order 2 III
The differential equation
.
has
as a solution. What are the values of
and
?
Give the exact values of the constants.
Given solutions II
We havea linear differential equation with constant coefficients
.
Knowing that the following two functions are solutions, determine this equation.
,
Homogeneous order 2 IC
Find the solution
of the differential equation
such that
and
. - Step 1.
- :
. - Step 2.
- :
{}. - Step 3.
-
| 2: |
|
| 3: |
|
| 4: |
|
where
and
are constants.
for all
- Step 4.
- The condition
gives
a condition on
and
which can be written :
Write C1 and C2 to denote respectively the constants
et
.
. - Step 5.
- And the condition
gives
Write the condition
by using the notations C1 and C2 without taking into account the condition given in step 4.
. - Step 6.
- Finally, these last two equations give
=
,
=
.
Give the exact values if necessary in the form of fractions.
In conclusion,
for all
is the desired solution.
Homogeneous order 2 type I
Find the solution
of the differential equation
such that
,
.
Homogeneous order 2 type II
Find the solution
of the differential equation
such that
,
.
Homogeneous order 2 type III
Find the solution
of the differential equation
such that
,
.
Homogeneous order 2 type IV
Find the solution
of the differential equation
such that
,
.
Homogeneous order 2 mixed type
Find the solution
of the differential equation
such that
and
.
Homogeneous order 2 by steps
The goal of the exercise is to find the form of the solutions of the differential equation
.
- Step 1.
- :
. - Step 2.
-
{}. - Step 3.
-
| 2: |
|
| 3: |
|
| 4: |
|
where
and
denote constants.
Limit of solution O2
Consider a differential equation
.
When this equation has
The non-existence of the limit means that even a limit as 
or - does not exist.
: for
.
. Choose "" to finish.
Polynomial solution order 1
Find the polynomial solution y=f(x) of the differential equation
.
Polynomial solution order 2
Find the polynomial solution
of the differential equation
.
Polynomial solution order 3
Find the polynomial solution
of the differential equation
.
Roots of solution O2
Consider a differential equation
.
When does this equation have a non-zero solution
having ?
: for
.
, because
This page is not in its usual appearance because WIMS is unable to recognize your
web browser.
Please take note that WIMS pages are interactively generated; they are not ordinary
HTML files. They must be used interactively ONLINE. It is useless
for you to gather them through a robot program.
- Description: collection of exercises on elementary ordinary differential equations. This is the main site of WIMS (WWW Interactive Multipurpose Server): interactive exercises, online calculators and plotters, mathematical recreation and games
- Keywords: wims, mathematics, mathematical, math, maths, interactive mathematics, interactive math, interactive maths, mathematic, online, calculator, graphing, exercise, exercice, puzzle, calculus, K-12, algebra, mathématique, interactive, interactive mathematics, interactive mathematical, interactive math, interactive maths, mathematical education, enseignement mathématique, mathematics teaching, teaching mathematics, algebra, geometry, calculus, function, curve, surface, graphing, virtual class, virtual classes, virtual classroom, virtual classrooms, interactive documents, interactive document, analysis, mathematics, ode, differential_equation,linear_differential_equation