Hola
4 en una pregunta...
u = y/x ; y = v x
dy = x dv + v dx ; y' = x v' + v
1)
x (vx + x) = (x^2 + v^2 x^2) (x v'+ v)
v + 1 = (1 + v^2) x v' + (v + v^3)
(1 + v^2) x dv/dx = 1 - v^3
(1 + v^2) dv/(1 - v^3) = dx/x
2)
y' = x sen(x+y)
u = x + y
u' = 1 + y'
u' - 1 = x sen(u)
NO, no es homogénea
3)
u = x - y
v = x + y
x = (1/2) v + (1/2) u
y = (1/2) v - (1/2) u
dy/dx = (dv - du)/(dv + du) = u/v
v dv - v du = u dv + u du
v dv - u du = u dv + v du
v^2 - u^2 = 2 u v + k
(x + y)^2 - (x - y)^2 = 2(x + y)(x - y) + k
4)
u = 7 x + 2 y
v = 2 x + 7 y
x = (7/45) u - (2/45) v
y = -(2/45) u + (7/45) v
dy/dx = (-2 du + 7 dv) / (7 du - 2 dv)
u (-2 du + 7 dv) / (7 du - 2 dv) = - v
- 2 u du + 7 u dv = - 7 du v + 2 v dv
7 (u dv + v du) - 2 u du - 2 v dv = 0
7 u v - u^2 - v^2 = k
7(7 x + 2 y)(2 x + 7 y) - (7 x + 2 y)^2 - (2 x + 7 y)^2 = k
NO ABRAN ES UN TROYANO!!!!!
o.o
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Answers & Comments
Verified answer
Hola
4 en una pregunta...
u = y/x ; y = v x
dy = x dv + v dx ; y' = x v' + v
1)
x (vx + x) = (x^2 + v^2 x^2) (x v'+ v)
v + 1 = (1 + v^2) x v' + (v + v^3)
(1 + v^2) x dv/dx = 1 - v^3
(1 + v^2) dv/(1 - v^3) = dx/x
2)
y' = x sen(x+y)
u = x + y
u' = 1 + y'
u' - 1 = x sen(u)
NO, no es homogénea
3)
u = x - y
v = x + y
x = (1/2) v + (1/2) u
y = (1/2) v - (1/2) u
dy/dx = (dv - du)/(dv + du) = u/v
v dv - v du = u dv + u du
v dv - u du = u dv + v du
v^2 - u^2 = 2 u v + k
(x + y)^2 - (x - y)^2 = 2(x + y)(x - y) + k
4)
u = 7 x + 2 y
v = 2 x + 7 y
x = (7/45) u - (2/45) v
y = -(2/45) u + (7/45) v
dy/dx = (-2 du + 7 dv) / (7 du - 2 dv)
u (-2 du + 7 dv) / (7 du - 2 dv) = - v
- 2 u du + 7 u dv = - 7 du v + 2 v dv
7 (u dv + v du) - 2 u du - 2 v dv = 0
7 u v - u^2 - v^2 = k
7(7 x + 2 y)(2 x + 7 y) - (7 x + 2 y)^2 - (2 x + 7 y)^2 = k
NO ABRAN ES UN TROYANO!!!!!
o.o