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 nonexistence 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 nonzero solution
having ?
: for
.
, because
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 Description: collection of exercises on elementary ordinary differential equations. serveur web interactif avec des cours en ligne, des exercices interactifs en sciences et langues pour l'enseigment primaire, secondaire et universitaire, des calculatrices et traceurs en ligne
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