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Determine the differential equation giving the slope of the tangent line at the point $(x, y)$ for the given family of curves.$$y=c e^{2 x}$$
$y^{\prime}=2 y$
Calculus 2 / BC
Chapter 1
First-Order Differential Equations
Section 3
The Geometry of First-Order Differential Equations
Differential Equations
Campbell University
Harvey Mudd College
Boston College
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All right. So we're looking for the differential equation, satisfied by the family of curves giving by y city to get your acts. This is a pretty simple problem. We just remember that the axe teach your axe. So seven defining property here you took the tracks is that it's derivative is two times itself. Andi. That means that's why prime is equal. Teoh see times to eat two acts. What is he quoted to your time See into the two X, which is just too Why? So the answer is that Why in prime singles twice wire for all of youse, for all wine and for all all of these cars we have Why Prime Nicholas True I and that's the differential equation that there's solved.
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