Differential Equations I
Differential Equations IMATB44H3FVersion September 15, 2011-1949iiContents1 Preliminaries. . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sample Application of Differential Equations . . . . . . . . . . .22 First Order Ordinary Differential Separable Equations . . . . . . . . . . . . . . . . . . . . . . . . . Exact Differential Equations . . . . . . . . . . . . . . . . . . . . . Integrating Factors. . . . . . . . . . . . . . . . . . . . . . . . . . Linear First Order Equations . . . . . . . . . . . . . . . . . . . . Substitutions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bernoulli Equation. . . . . . . . . . . . . . . . . . . . . . Homogeneous Equations . . . . . . . . . . . . . . . . . . . Substitution to Reduce Second Order Equations to FirstOrder. . . . . . . . . . . . . . . . . . . . . . . . . . . . .203 Applications and Examples of First Orderode Orthogonal Trajectories.
1.2. SAMPLE APPLICATION OF DIFFERENTIAL EQUATIONS 3 Sometimes in attempting to solve a de, we might perform an irreversible step. This might introduce extra solutions.
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