Download - MAT 2998J.M. Lina
![Page 1: MAT 2998J.M. Lina](https://reader036.vdocuments.us/reader036/viewer/2022083006/56813f29550346895da9c788/html5/thumbnails/1.jpg)
MAT 2998 J.M. Lina
EQUATION DIFF. ORD. SECOND ORDRE
)()()( trytqytpy
)(tdt
dyy
)(2
2
tdt
ydy
)()()( trytqytpy = 0
Équation homogène:
0 ybyayÉquation à coefficients constants
![Page 2: MAT 2998J.M. Lina](https://reader036.vdocuments.us/reader036/viewer/2022083006/56813f29550346895da9c788/html5/thumbnails/2.jpg)
MAT 2998 J.M. Lina
)(tdt
dyy
)(2
2
tdt
ydy
0 ybyay
Équation à coefficients constants
)()()( 2211 tyctycty Solution de la forme:
tety )( dans 0 ybyay
02 baou
0))(( 21
ba 42
et racines dupolynôme caractéristique
![Page 3: MAT 2998J.M. Lina](https://reader036.vdocuments.us/reader036/viewer/2022083006/56813f29550346895da9c788/html5/thumbnails/3.jpg)
MAT 2998 J.M. Lina
)(tdt
dyy
)(2
2
tdt
ydy
0 ybyay
Équation à coefficients constants
• cas 1: 042 ba
tt ececty 2121)(
baa
baa
42
1
2
42
1
2
22
21
![Page 4: MAT 2998J.M. Lina](https://reader036.vdocuments.us/reader036/viewer/2022083006/56813f29550346895da9c788/html5/thumbnails/4.jpg)
MAT 2998 J.M. Lina
)(tdt
dyy
)(2
2
tdt
ydy
0 ybyay
Équation à coefficients constants
• cas 2: 042 ba
)()( 211 ctcety t
221
a
![Page 5: MAT 2998J.M. Lina](https://reader036.vdocuments.us/reader036/viewer/2022083006/56813f29550346895da9c788/html5/thumbnails/5.jpg)
MAT 2998 J.M. Lina
)(tdt
dyy
)(2
2
tdt
ydy
0 ybyay
Équation à coefficients constants
• cas 3: 042 ba
)()( 212 titita
ececety
ia
ia
2
2
2
1
22
2
42
1
ab
ab
![Page 6: MAT 2998J.M. Lina](https://reader036.vdocuments.us/reader036/viewer/2022083006/56813f29550346895da9c788/html5/thumbnails/6.jpg)
MAT 2998 J.M. Lina
)()( 212 titita
ececety
Belouzov
)cos(2
2
121
tee
cc
titi
)12cos( te t
![Page 7: MAT 2998J.M. Lina](https://reader036.vdocuments.us/reader036/viewer/2022083006/56813f29550346895da9c788/html5/thumbnails/7.jpg)
MAT 2998 J.M. Lina
)()()( trytqytpy )(tdt
dyy
)(2
2
tdt
ydy
t
t
ekty
cetr
)(typedesolution
)(
)sin()cos()(typedesolution
)cos()(
21 tktkty
tctr
)sin()cos()(typedesolution
)cos()(
21 tektekty
tcetrtt
t