Particular Solutions

AP Calculus · Axiom Academy

Using initial conditions to find the specific solution to a DE General vs. Particular Solutions The general solution of a DE contains an arbitrary constant C and represents a family of curves. A particular solution satisfies a specific initial condition y(x_0) = y_0 , which pins down C . General: y = x^2 + C . Substituting: . This means solution curves in a slope field never cross (as long as the conditions hold). Solve the DE for the general solution, then plug in the IC to find C IVPs (Initial Value Problems) have unique solutions under mild conditions On the AP exam, always state the particular solution with its domain

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