- #1
Lo.Lee.Ta.
- 217
- 0
The differential equation I'm working on is:
4(√(xy))dy/dx=1, y(1)=1
(√(xy)dy/dy)2 = (1/4)2
((xy)dy/dx)*dx = (1/8)*dx
(xy)dy = (1/8)dx
(y)dy = (1/(8x))dx
...So I think this is right so far.
Now I'm going to take the integral of both sides.
∫(y)dy = ∫(1/(8x))dx <------∫(1/x)(1/8)dx
1/2y2 = ln|x|*(1/8) + C
√[y2] = √[2(ln|x|*(1/8) + C)]
y= √(1/4*ln|x| + C)
...Substitution in the y(1)=1
1 = √(1/4*ln|1| + C)
4 = 0 + C
C = 4
y(x)= √(1/4*ln|x| + 4)
This is counted as the wrong answer, but I don't know what I'm doing wrong here... #=_=
Thank you so much!
4(√(xy))dy/dx=1, y(1)=1
(√(xy)dy/dy)2 = (1/4)2
((xy)dy/dx)*dx = (1/8)*dx
(xy)dy = (1/8)dx
(y)dy = (1/(8x))dx
...So I think this is right so far.
Now I'm going to take the integral of both sides.
∫(y)dy = ∫(1/(8x))dx <------∫(1/x)(1/8)dx
1/2y2 = ln|x|*(1/8) + C
√[y2] = √[2(ln|x|*(1/8) + C)]
y= √(1/4*ln|x| + C)
...Substitution in the y(1)=1
1 = √(1/4*ln|1| + C)
4 = 0 + C
C = 4
y(x)= √(1/4*ln|x| + 4)
This is counted as the wrong answer, but I don't know what I'm doing wrong here... #=_=
Thank you so much!