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nikdorinn [45]
3 years ago
9

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

Mathematics
1 answer:
Alex777 [14]3 years ago
7 0

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}}

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