Find a solution of xdydx=y2−y that passes through the indicated points. a. (0,0) b. (14,14)...

Adela Brown

Adela Brown

Answered

2021-12-22

Find a solution of xdydx=y2y that passes through the indicated points.
a. (0,0)
b. (14,14)
c. (6,18)

Answer & Explanation

Melissa Moore

Melissa Moore

Expert

2021-12-23Added 32 answers

By separing variables in xdydx=y2y; we have
dyy2y=dxx
dyy(y1)=dxx
[1y]+1y1]dy=dxx
On integration, we obtain
ln(y)+ln(y1)=ln(x)+lnc
ln(y1y)=ln(xc)
y1y=xc
y1=xyc
yxyc
y(1xc)=1
y=11xc
y=11cx is a solution and y=0 is another constant solution
a) At (0,0)
y=11xc
0=110
0=1
This is not possible
Therefore in this case there is no solution.
karton

karton

Expert

2021-12-30Added 439 answers

c) At (6,18)
Here, x=6,y=18
18=116c
16c=8
Substitute c=76 in y=11cx
Thus,
y=11+76x
=66+7x
The solution of the initial value problem is y=66+7x

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