Different Equations

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Students will 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.

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