Ecuaciones lineales y no lineales
Enviado por TMXmaik • 22 de Abril de 2022 • Trabajos • 1.281 Palabras (6 Páginas) • 67 Visitas
Universidad tecnológica de chihuahua
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Matemáticas para ingeniería II
Evidencia 1.3.2 (ED Lineales y ED No lineales – Bernoulli)
Alumno: Eduardo Santana Estrada
Matricula: 1119130140
Grupo: IMI83M
Docente: I.C. Gloria Hernández
Fecha: 13/02/2022
Evidencia 1.3.2 (ED Lineales y ED No lineales – Bernoulli)
𝐸𝐷 𝐿𝑖𝑛𝑒𝑎𝑙 | 𝐸𝐷 𝑁𝑜 𝐿𝑖𝑛𝑒𝑎𝑙 − 𝐵𝑒𝑟𝑛𝑜𝑢𝑙𝑙𝑖 | ||||
𝐹𝑜𝑟𝑚𝑎 𝑔𝑒𝑛𝑒𝑟𝑎𝑙 | 𝒚′ | + 𝒑(𝒙)𝒚 = 𝒒(𝒙) | 𝒖′ + 𝒑(𝒙) 𝒖 = 𝒒(𝒙) | ||
𝐹𝑎𝑐𝑡𝑜𝑟 𝑖𝑛𝑡𝑒𝑔𝑟𝑎𝑛𝑡𝑒 | 𝝁(𝒙) = 𝒆∫ 𝒑(𝒙) 𝒅𝒙 | 𝝁(𝒙) = 𝒆∫ 𝒑(𝒙) 𝒅𝒙 | |||
𝑆𝑜𝑙𝑢𝑐𝑖ó𝑛 𝑔𝑒𝑛𝑒𝑟𝑎𝑙 | 𝝁 𝒚 = ∫ 𝝁 𝒒 𝒅𝒙 | 𝒖 𝝁 = ∫ 𝒒 𝝁 𝒅𝒙 | |||
𝐸𝐷 𝑁𝑜 𝐿𝑖𝑛𝑒𝑎𝑙 − 𝐵𝑒𝑟𝑛𝑜𝑢𝑙𝑙𝑖 | 𝑷𝟎(𝒙) | 𝒅𝒚 [pic 2] 𝒅𝒙 | + 𝑷𝟏(𝒙) 𝒚 = 𝑸(𝒙) 𝒚𝒏 | 𝑆𝑢𝑠𝑡𝑖𝑡𝑢𝑐𝑖ó𝑛 | 𝒖 = 𝒚𝟏−𝒏 |
En las siguientes ecuaciones diferenciales determine la solución general o particular según sea el caso.
𝟎𝟏. 𝒚′ + 𝟑𝒙𝟐𝒚 = 𝒙𝟐 𝑹 → 𝒚 = 𝟏 + 𝑪𝒆−𝒙𝟑[pic 3]
𝟑
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𝟎𝟐. 𝒚 𝒅𝒙 − 𝟒(𝒙 + 𝒚𝟔) 𝒅𝒚 = 𝟎 𝑹 → 𝒙 = 𝟐𝒚𝟔 + 𝑪𝒚𝟒
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𝟎𝟑. 𝒄𝒐𝒔 𝒙
𝒅𝒚
[pic 20]
𝒅𝒙
+ (𝒔𝒆𝒏 𝒙) 𝒚 = 𝟏 𝑹 → 𝒚 = 𝒔𝒆𝒏 𝒙 + 𝑪 𝒄𝒐𝒔
[pic 21]
𝟎𝟒. 𝒙 𝒅𝒚 + (𝟑𝒙 + 𝟏)𝒚 = 𝒆−𝟑𝒙 𝑹 → 𝒚 = 𝒆−𝟑𝒙 + 𝑪𝒙−𝟏 𝒆−𝟑𝒙[pic 22]
𝒅𝒙
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𝟎𝟓. 𝒙𝒚′ + 𝒚 = 𝒆𝒙, 𝒚(𝟏) = 𝟐 𝑹 → 𝒚 = 𝒙−𝟏𝒆𝒙 + (𝟐 − 𝒆)𝒙−𝟏
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=[pic 40][pic 41]
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yx=[pic 43]
Y=[pic 44]
y(1)=2, x=1, y=2
2=e+C C=2-e[pic 45]
Y=[pic 46]
𝟎𝟔. (𝒙 + 𝟏)
𝒅𝒚
[pic 47]
𝒅𝒙
+ 𝒚 = 𝒍𝒏 𝒙 , 𝒚(𝟏) = 𝟏𝟎 𝑹 → (𝒙 + 𝟏)𝒚 = 𝒙 𝒍𝒏 𝒙 − 𝒙 + 𝟐𝟏
[pic 48]
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)=[pic 50][pic 51]
[pic 52]
Y(x+1)=xlnx-x+C
Y(1)=10, x=1, y=10
10(2)=(1)ln(1)-1+C
20=-1+C C=21[pic 53]
Y(x+1)=xlnx-x+21
𝟎𝟖. 𝒅𝒚 − 𝒚 = 𝒆𝒙𝒚𝟐 𝑹 → 𝒚 = 𝟏[pic 54][pic 55]
𝒅𝒙
𝑪𝒆−𝒙 − 𝟏 𝒆𝒙
𝟐
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[pic 57][pic 58]
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