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Differential Equations
A differential equation relates a quantity to its own rate of change — which is how every law of physics is stated. The solver names the method (separable, integrating factor, characteristic equation), solves, verifies by substitution, and draws the family of solutions.
Lecții
Core
Separable equations
dy/dx = f(x)g(y): separate, integrate both sides, solve for y.
y' = 2y
Core
First-order linear equations
y′ + P(x)y = Q(x) and the integrating factor that makes it integrable.
y' + y = x
Core
Second-order, constant coefficients
ay″ + by′ + cy = 0 and the characteristic equation: oscillation, damping, growth.
y'' + y = 0
Advanced
Nonhomogeneous equations
Driving forces: homogeneous solution plus a particular solution.
y'' - 3y' + 2y = e^x
Core
Modelling with differential equations
Growth, decay, cooling, mixing: writing the equation from the sentence.
y' = 0.05*y
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