Solved: Determine the stress components acting on the inclined plane AB. Solve the

ENGR 232 Dynamic Engineering Systems Lecture 3 Dr. Michael Ryan Agenda • Quick Review – Integrating factor • First Order Differential Equations – Existence – Models • Second Order Differential Equations – Models – Homogeneous equations – Auxiliary equation and its roots – Unique solutions 2 Integrating Factor Method General Case Process a) Write the equation in standard form and identify terms b) Calculate the integrating factor c) Multiply both sides of the equation by the integrating factor. ▯▯ ▯ ▯ ▯▯ + ▯ ▯ ▯ = ▯ ▯ ▯(▯) d) Recognizing the left side as the derivative of product: ▯▯ ▯ ▯ ▯ ▯ ▯ ▯ + ▯ ▯ ▯ = =▯ ▯ ▯(▯) ▯▯ ▯▯ e) Integrate ▯ ▯ ▯= ▯ ▯ ▯ ▯ ▯ f) Then solve for y(t) and use ICs is present 4/13/2015 ENGR 232 Spring14 - 15 Week 3 3 Integrating Factor for 1 st Order Linear D.E. ▯▯ ▯▯+ ▯ ▯ ▯ = ▯(▯) ▯ 0 = ▯ ▯ Form of D.E. Integrating factor Solution ▯▯ ▯▯ ▯▯▯ ▯▯ ▯▯▯ + ▯▯ = ▯ ▯(▯) = ▯ y ▯ = ▯ ▯ ▯ ▯▯▯ + ▯▯ ▯▯ y ▯ = ▯ + ▯ ▯▯ ▯ e ▯▯▯