A differential equation is given by ${\displaystyle \frac{\mathrm{d}y}{\mathrm{d}x}=\frac{x^6-e^xy}{e^x}.}$

(a) Use the substitution ${z=e^xy}$ to show that the differential equation can be reduced into the form ${\displaystyle\frac{\mathrm{d}z}{\mathrm{d}x}=f(x)}$, where ${f(x)}$ is a function to be determined.

(b) Hence solve the differential equation to find ${y}$ in terms of ${x}$, given that ${y=7} \allowbreak \textrm{ when } \allowbreak {x=0}.$

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