Actividad virtual 4- ecuaciones diferenciales
Enviado por solange0618 • 29 de Marzo de 2022 • Exámen • 458 Palabras (2 Páginas) • 326 Visitas
ACTIVIDAD VIRTUAL 2 ECUACIONES DIFERENCIABLES
[pic 1]
SOLUCIÓN
[pic 2]
𝑦3
a) (𝑦 +[pic 3][pic 4][pic 5]
) = 𝑥
+ 𝑐
3
𝑦3
b) (𝑦 +[pic 6]
4
𝑦3
c) (𝑦 +[pic 7]
3
4
3
) = 𝑥3[pic 8]
3
) = 𝑥3[pic 9]
4
𝑥3
+ 𝑐
+ 𝑐
d) (𝑦 +
) =
3[pic 10]
𝑦3
+ 𝑐
3[pic 11]
𝑥3
e) (2𝑦 + ) =[pic 12]
3
+ 𝑐
3[pic 13]
[pic 14]
SOLUCIÓN
[pic 15]
𝑦2
A) 2𝑦 −[pic 16][pic 17][pic 18]
= 𝑥
+ 𝑥 + 12
2
𝑦2
B) 2𝑦 −[pic 19]
2
𝑦2
C) 2𝑦 −[pic 20]
2
𝑦2
D) 7𝑦 −[pic 21]
2
𝑦2
E) 7𝑦 −[pic 22]
2
3
= 𝑥3
[pic 23]
3
= 𝑥3
[pic 24]
3
= 𝑥3
[pic 25]
3
= 𝑥3
[pic 26]
3
+ 𝑥 + 14
+ 2𝑥 + 12
+ 𝑥 + 13
+ 𝑥 + 14
[pic 27]
SOLUCIÓN
[pic 28]
[pic 29]
A) 1 [(𝑥 + 2𝑦) + 𝑠𝑒𝑛2(𝑥+2𝑦)] = 𝑥 + 𝐶
2 2[pic 30][pic 31]
B) 1 [(𝑥 + 3𝑦) + 𝑠𝑒𝑛2(𝑥+2𝑦)] = 2𝑥 + 𝐶[pic 32][pic 33]
2 2
C) 1 [(𝑥 + 2𝑦) + 𝑠𝑒𝑛2(𝑥+2𝑦)] = 8𝑥 + 𝐶[pic 34][pic 35]
2 3
D) 1 [(𝑥 + 2𝑦) + 𝑠𝑒𝑛2(𝑥+2𝑦)] = 5𝑥 + 𝐶[pic 36][pic 37]
2 2
[pic 38]
SOLUCIÓN
[pic 39]
[pic 40]
A) − 𝑥[pic 41]
𝑦
B) − 𝑥[pic 42]
𝑦
= 𝑙𝑛𝑥 − 1
= 𝑙𝑛𝑥 − 2
−
- −
2𝑥
[pic 43]
𝑦
𝑥
[pic 44]
2𝑦
𝑥
= 𝑙𝑛𝑥 − 1
= 𝑙𝑛𝑥 − 1
−[pic 45]
𝑦
= 2𝑙𝑛𝑥 − 1
[pic 46]
[pic 47][pic 48]
- tan
- tan
𝑦 = ln 𝑥 + 𝐶
𝑥[pic 49]
𝑦 = ln 𝑥 + 1[pic 50]
- tan
- tan
- tan
2𝑥
𝑦 = ln 𝑥 + 2[pic 51]
𝑥
𝑦 = 2 ln 𝑥 + 1[pic 52]
𝑥
𝑦 = 2 ln 𝑥 + 𝐶[pic 53]
𝑥
[pic 54]
SOLUCIÓN
[pic 55]
[pic 56]
A) 𝑦 = 𝑘√𝑥2 + 4
[pic 57]
B) 𝑦 = 2𝑘√𝑥2 + 4[pic 58]
C) 𝑦 = 𝑘√2𝑥2 + 4
[pic 59]
D) 𝑦 = 𝑘√𝑥2 + 8[pic 60]
E) 𝑦 = 𝑘√2𝑥2 + 8
[pic 61]
[pic 62][pic 63]
A) 𝑦 = √𝑥2 + 𝐶
[pic 64]
B) 𝑦 = 2√𝑥2 + 𝐶[pic 65]
...