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
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- Description: collection of exercises on elementary ordinary differential equations. interactive exercises, online calculators and plotters, mathematical recreation and games
- Keywords: interactive mathematics, interactive math, server side interactivity, analysis, mathematics, ode, differential_equation,linear_differential_equation