(Solved): the rate of 3gal/min. Find the solution to the differential equation that models the mixing proces ...

the rate of $$3\mathrm{gal}/\min$$. Find the solution to the differential equation that models the mixing process. $$\text{ a. }y=4(50+t)?\frac{C}{(100+t{)}^3}$$ b. $$y=4(50+t)?\frac{10^8}{(100+t{)}^3}$$ $$\text{ c. }y=2(100+t)?\frac{C}{\left(100+t^3\right)}$$ d. $$y=2(100+t)?\frac{10^8}{(100+t{)}^3}$$ Determine if the given function $$y=f(x)$$ is a solution of the accompanying differential equation. $$\begin{array}{l}{y}^{?}?y=8e^x\\ y=e^{8x}+8x{e}^x\end{array}$$ a. Yes b. No QUESTION 10 Solve. Solve the initial value problem $$\frac{\mathrm{dP}}{\mathrm{dt}}=3\mathrm{kP}{}^2,P(0)=P_0$$ a. $$P(t)=\frac{3P_0}{1?3k{P}_{0}t}$$ b. $$P(t)=\frac{P_0}{1?k{P}_{0}t}$$ c. $$P(t)=\frac{P_0}{1?3k{P}_{0}t}$$ d. $$P(t)=\frac{P_0}{3?3k{P}_{0}t}$$