MATH 1005 Study Guide - Final Guide: Integrating Factor, Second Order (Religious)
23 Apr 2015
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Some little things to always remember: y"= dy dx ealn(x)=xa. Orthogonal trajectory: solve for the constant, take (*second also if asks for 2 families *) derivative of y with respect to x, plug solution for constant into derivative and simplify, take the negative inverse of the derivative. Note: if you are given a y" equation just go straight to step 4. An equation of the form (*or that can be put into the form*): dy dx. *always separate variables and solve if you can* - that"s the easy way out. 1. (*remember it is a function of x and not y*: evaluate: p ( x)dx *(easier to do this first before next step), define integrating factor. I ( x)=e p( x) dx: solution: multiply the equation by i ( x) and put into this form: [ yi ( x)]"=q ( x) i ( x)
