Solve the decay equation y' = -ky using the integrating factors method. Show work

asked Apr 13, 2020 203k views

4 votes

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4 votes

Answer:

y=(c)/(e^(kx))

Explanation:

$\frac{\mathrm{d} y}{\mathrm{d} x} =-ky$

$\frac{\mathrm{d} y}{\mathrm{d} x} +ky=0$

comparing with equation

$\frac{\mathrm{d} y}{\mathrm{d} x} + Py=Q(x)$

$I.F.= e^(\int P dx)$

$I.F.= e^(\int k dx)$

I.F.= e^(kx)

$y=(1)/(I.F.) ( \int {Q(x)}  dx  +c)$

$y=(1)/(e^(kx)) ( \int {0}  dx  +c)$

y=(c)/(e^(kx))

Nguyen Hoan answered Apr 18, 2020

5.8k points

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