Give a differential equation satisfied by P=400e^(.4t) y'= ____(y)
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Originally Posted by v3ndetta Give a differential equation satisfied by P=400e^(.4t) y'= ____(y) Since $\displaystyle P=400e^{.4t}$, $\displaystyle \frac{\,dP}{\,dt}=400e^{.4t}\cdot.4=.4\left(400e^{ .4t}\right)=.4P$ Therefore, we can conclude that a possible differential equation that is satisfied by $\displaystyle P=400e^{.4t}$ is $\displaystyle P^{\prime}=.4P$.
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