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Simple differential equation problem I am having trouble with?
Solve the separable linear fi rst order DE: dy/dx -4xy =0
using both the method of separation of variables and using an integrating factor.
I can solve it using the separation of variables technique, I'm just having trouble with the integration factor method.
4 Answers
- iyiogrenciLv 68 years ago
dy/dx -4xy =0
dy=4xydx
dy/y=4xdx
by integrating both sides
ln y = 4 x^2/2 +C
ln y= 2x^2+C
y= e^(2x^2+C)
- Anonymous8 years ago
dy/dx - 4xy = 0
Compare with : dy/dx + Py = Q
P = -4x Q=0
I = e^(Pdx) = e^(-2x^2)
Solution is:
yI = (QI)dx = 0dx = c
y * e^(-2x^2) = c
Taking log on both sides
lny -2x^2 = lnc
lny = 2x^2 + k
where k is a constant
- Anonymous8 years ago
dy/dx=4xy
dy/y=4xdx
ln y=2x^2
y=(e^2x^2)+c
- ?Lv 78 years ago
y' - 4xy = 0
µ = e^(∫-4x dx)
µ = e^(-2x^2)
e^(-2x^2)y' - 4xye^(-2x^2) = 0
∫ d/dx(ye^(-2x^2))dx = ∫0dx
ye^(-2x^2) = 0 + c
y = ce^(2x^2)
