Question

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

Answer 1

Answer:

$y=\frac{c}{e^{kx}}$

Step-by-step explanation:

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

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

comparing with equation

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

$I.F.= e^{\int P dx}$

$I.F.= e^{\int k dx}$

$I.F.= e^{kx}$

$y=\frac{1}{I.F.} ( \int {Q(x)}  dx  +c)$

$y=\frac{1}{e^{kx}} ( \int {0}  dx  +c)$

$y=\frac{c}{e^{kx}}$