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JuanCarlosMM123Documentos de Investigación2 de Abril de 2022
11.923 Palabras (48 Páginas)135 Visitas
UNIVERSIDAD AUTONOMA DE NUEVO LEON[pic 1][pic 2]
FACULTAD DE INGENIERIA MECANICA Y ELECTRICA
PRODUCTO INTEGRADOR DE APRENDIZAJE
Ing. Christian Fabian Chapa Arce
Matrícula | Nombre | Carrera |
1898301 | Gil Briones Arely Maricruz | IMA |
1899068 | Uribe Guerrero Edgar Alejandro | IMTC |
1899715 | Sanchez Chapa Miguel Angel | IMA |
1900335 | Correa Aleman Claudia Yaneth | IMA |
1902531 | Urias Sanchez Valeria | IAS |
Grupo: 038
Actividad fundamental #1
Orden, grado, linealidad
𝑑2𝑦
1) 𝑑𝑥2[pic 3]
+ 13 (
𝑑𝑦 5
𝑑𝑥)[pic 4]
+ 𝑥2 = (
𝑑𝑦 3
𝑑𝑥)[pic 5]
Ordinaria; Orden 2; Grado 1; No lineal
[pic 6]
𝑑3𝑦
2) √[pic 7][pic 8]
𝑑𝑥
− 5𝑥 = 8 (
𝑑𝑦
𝑑𝑥)[pic 9]
𝑑3𝑦
[pic 10]
𝑑𝑥3[pic 11]
− (5𝑥)2 = (8 (
2
𝑑𝑦
𝑑𝑥))[pic 12]
Ordinaria; Orden 3; Grado 1; No lineal
3) (
𝑑4𝑦
[pic 13]
𝑑𝑥4
3 𝑑3𝑦
) 𝑑𝑥3[pic 14]
𝑑2𝑦
+ 𝑑𝑥2[pic 15]
− 𝑦2 = 0
Ordinaria; Orden 4; Grado 3; No lineal[pic 16]
[pic 17] [pic 18]
𝑑2𝑦
5 𝑑3𝑦 3
𝑑2𝑦
5 𝑑3𝑦 6
4) √[pic 19]
𝑑𝑥
+ 3𝑥 = √( )
𝑑𝑥3[pic 20][pic 21]
(
𝑑𝑥[pic 22]
2 + 3𝑥)
= ( )
𝑑𝑥3[pic 23]
𝑂𝑟𝑑𝑖𝑛𝑎𝑟𝑖𝑎; 𝑂𝑟𝑑𝑒𝑛 3; 𝐺𝑟𝑎𝑑𝑜 6; 𝑁𝑜 𝑙𝑖𝑛𝑒𝑎𝑙
5) 𝑑2𝑦 + 𝑘2𝑦 = 0[pic 24]
𝑑𝑥2
𝑂𝑟𝑑𝑖𝑛𝑎𝑟𝑖𝑎; 𝑂𝑟𝑑𝑒𝑛 2; 𝐺𝑟𝑎𝑑𝑜 1; 𝐿𝑖𝑛𝑒𝑎𝑙
𝑥2 + 𝑦2
6) (𝑥2 + 𝑦2)𝑑𝑥 − 2𝑥𝑦𝑑𝑦 = 0[pic 25][pic 26]
2𝑥𝑦
𝑑𝑦
= 𝑑𝑥[pic 27]
𝑂𝑟𝑑𝑖𝑛𝑎𝑟𝑖𝑎; 𝑂𝑟𝑑𝑒𝑛 1; 𝐺𝑟𝑎𝑑𝑜 1; 𝑁𝑜 𝑙𝑖𝑛𝑒𝑎𝑙
P1-Comprobación de una ecuación diferencial
1) 𝑦 = 𝑐2 + 𝑐𝑥−1, 𝑦 + 𝑥𝑦´ = 𝑥4(𝑦´)2
𝑥4(𝑦´)2 − 𝑥𝑦´ − 𝑦 = 0
𝑑𝑦 𝑐
[pic 28] [pic 29]
4 𝑐 2
[pic 30]
𝑐 2 −1
[pic 31]
𝑑𝑥 = 0 + 𝑥
𝑥 (− 𝑥)
− 𝑥 (− 𝑥2) − 𝑐 − 𝑐𝑥 = 0
𝑑𝑦
[pic 32]
𝑥 ∗ 0 − 𝑐 ∗ 1
=[pic 33]
𝑥4 (
𝑐2 𝑐
) +[pic 34][pic 35]
− 𝑐2 − 𝑐 = 0
𝑑𝑥[pic 36]
𝑥2
𝑥4 𝑥 𝑥
𝑑𝑦 𝑐
= −[pic 37][pic 38]
𝑐2 + 𝑐 − 𝑐2 − 𝑐 = 0
[pic 39] [pic 40]
𝑑𝑥
𝑥2
𝑥 𝑥
𝑆í 𝑒𝑠 𝑢𝑛𝑎 𝑠𝑜𝑙𝑢𝑐𝑖ó𝑛 𝑔𝑒𝑛𝑒𝑟𝑎𝑙
0 = 0
2) 𝑒cos(𝑥)(1 − cos(𝑦)) = 𝑐, 𝑠𝑒𝑛(𝑦) (𝑑𝑦) + 𝑠𝑒𝑛(𝑦) cos(𝑦) = 𝑠𝑒𝑛(𝑥)[pic 41]
𝑑𝑥
𝑐
1 − cos(𝑦) = 𝑒cos(𝑥)[pic 42]
𝑐 cos(𝑦) = 1 − 𝑒cos(𝑥)[pic 43]
−𝑠𝑒𝑛(𝑦) 𝑑𝑦 = 0 − (0 + (𝑐𝑠𝑒𝑛(𝑥)𝑒− cos(𝑥)))[pic 44]
𝑑𝑥
𝑑𝑦
𝑑𝑥 =[pic 45]
𝑐𝑒− cos(x)𝑠𝑒𝑛(𝑥)
[pic 46]
𝑠𝑒𝑛(𝑦)
𝑠𝑒𝑛(𝑦) ((𝑐𝑒−𝑐𝑜𝑠𝑥𝑠𝑒𝑛(𝑥))) 𝑐
𝑠𝑒𝑛(𝑦) + 𝑠𝑒𝑛(𝑦) (1 − 𝑒cos(𝑥)) − 𝑠𝑒𝑛(𝑥) = 0[pic 47][pic 48]
𝑐𝑒− cos(𝑥)𝑠𝑒𝑛(𝑥) + 𝑠𝑒𝑛(𝑦) − 𝑐𝑒− cos(𝑥)𝑠𝑒𝑛(𝑦) − 𝑠𝑒𝑛(𝑥) = 0
𝑁𝑜 𝑒𝑠 𝑢𝑛𝑎 𝑠𝑜𝑙𝑢𝑐𝑖ó𝑛 𝑔𝑒𝑛𝑒𝑟𝑎𝑙
3) 𝑦 = 8𝑥5 + 3𝑥2 + 𝑐,
𝑑𝑦 = 40𝑥4 + 6𝑥[pic 49]
𝑑𝑥
𝑑2𝑦
𝑑2𝑦
[pic 50]
𝑑𝑥2
− 6 = 160𝑥3
[pic 51]
𝑑𝑥2
...