Question

Given that y=1 when x=0, solve the equation

dy/dx= y(4-y)
Obtaining an expression for y in terms of x

Answer 1

the first step to solving an initial value differential equation is that you must separate the variable ;)

Answer 2

re-arrange :
dx = dy/(y(4-y))
integrate both sides..a constant will come up ..
use y=1 for x= 0 and find constant..thus you get the soln..

Answer 3

How to integrate both sides?

Answer 4

∫dx=∫dy/(y(4-y))

Answer 5

1/(4y - y^2 ) = (4-2y)/(4y - y^2) + (-3 + 2y)/(4y-y^2)
the second one can be done with more than 1 methods..use partial differentiation..
in first one..note that d/dy(denominator) = numerator..
hope this helps..

Answer 6

Partial fractions
\[\frac{1}{y(4-y)}=1/4(\frac{1}{y}+\frac{1}{4-y})\]

Answer 7

x+C=∫dy/(4-(y-2)^2); that is obtained by completing the square

Answer 8

Integrate
\[x=\frac{1}{4}[\ln(y)-\ln(4-y)]+c\]
Put x,y=(0,1)to find c

Answer 9

Is that all?

Answer 10

Pretty much

Answer 11

Is this the same? y = 4 /(3 e^−4x + 1)?