Question

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

Answer 1

`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))`