MAMC.D.9

MAMC.D.9: use, apply, and solve linear first-order differential equations; solve linear first-order differential equations of the form y' + p(x)y = q(x) with an integrating factor; solve homogeneous linear first-order differential equations using a variable substitution; solve Clairaut equations; explore the concepts of families of solutions and envelopes; write linear first-order differential equations that represent real-world phenomena and solve them, such as those arising from Kirchhoff's Law and mixing problems; students will solve linear second-order differential equations of the form y''+ p(x)y' + q(x)y = c using the characteristic equation where the characteristic equation has two real roots, one real root, or no real roots