Answer:
[tex]y=\frac{c}{e^{kx}}[/tex]
Step-by-step explanation:
[tex]\frac{\mathrm{d} y}{\mathrm{d} x} =-ky[/tex]
[tex]\frac{\mathrm{d} y}{\mathrm{d} x} +ky=0[/tex]
comparing with equation
[tex]\frac{\mathrm{d} y}{\mathrm{d} x} + Py=Q(x)[/tex]
[tex]I.F.= e^{\int P dx}[/tex]
[tex]I.F.= e^{\int k dx}[/tex]
[tex]I.F.= e^{kx}[/tex]
[tex]y=\frac{1}{I.F.} ( \int {Q(x)} dx +c)[/tex]
[tex]y=\frac{1}{e^{kx}} ( \int {0} dx +c)[/tex]
[tex]y=\frac{c}{e^{kx}}[/tex]
