# Thread: Help making a differential equation

1. ## Help making a differential equation

Give a differential equation satisfied by
P=400e^(.4t)
y'= ____(y)

2. Originally Posted by v3ndetta
Give a differential equation satisfied by
P=400e^(.4t)
y'= ____(y)
Since $P=400e^{.4t}$, $\frac{\,dP}{\,dt}=400e^{.4t}\cdot.4=.4\left(400e^{ .4t}\right)=.4P$

Therefore, we can conclude that a possible differential equation that is satisfied by $P=400e^{.4t}$ is $P^{\prime}=.4P$.