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10 cards from this deck
An equation involving the first derivative of an unknown function.
Separate variables, integrate both sides, solve for yyy.
dydx+P(x)y=Q(x)\frac{dy}{dx} + P(x)y = Q(x)dxdy+P(x)y=Q(x).
It simplifies a linear differential equation for integration.
They involve the second derivative of the unknown function.
Substitute y=emxy = e^{mx}y=emx into the differential equation.
The nature of the roots of the characteristic equation.
Relate it back to the physical context of the problem.
They help find specific values for constants in the solution.
It provides insight into the system's long-term behavior.
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