I noticed your equations when you posted them several days ago. I do not see how they can be solved by separation of variables. There are too many terms that involve both x and y.
Both problems are too difficult for me to find a closed-form solution.
variable saparable(separation of variable)
1.) (2x+y)dy + (2x+y+6)dx=0
2.)(5t+1)t ds + (25t-1)sdt=0
I don't the solution of this problem I think it a "repeated expression". Can someone help me on this? thanks a lot. :)
2 answers
2) (5t+1)t ds + (25t-1)sdt=0
Divide by (5t+1)ts :
ds/s + (25t-1)/[(5t+1)t]dt=0
1) (2x+y)dy + (2x+y+6)dx=0
Change of variables:
u = 2x+y
v = x
Then
y = u - 2 v
x = v
dy = du - 2 dv
dx = dv
1) becomes:
u (du - 2 dv) + (u+6)dv = 0 ------>
u du + (6 - u)dv = 0
Divide by (6-u):
u/(6-u) du + dv = 0
Divide by (5t+1)ts :
ds/s + (25t-1)/[(5t+1)t]dt=0
1) (2x+y)dy + (2x+y+6)dx=0
Change of variables:
u = 2x+y
v = x
Then
y = u - 2 v
x = v
dy = du - 2 dv
dx = dv
1) becomes:
u (du - 2 dv) + (u+6)dv = 0 ------>
u du + (6 - u)dv = 0
Divide by (6-u):
u/(6-u) du + dv = 0
1 answer