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Differential Equations I

Differential Equations IMATB44H3 FVersion 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.. Exponential Growth and Decay.. Population Growth.. Predator-Prey Models.. Newton s Law of Cooling.. Water Tanks.. Motion of Objects Falling Under Gravity with Air Resistance.. Escape Velocity.. Planetary Motion.. Particle Moving on a Curve..39iiiivCONTENTS4 Linear Differential Homogeneous Linear Equations .. Linear Differential Equations with Constant Nonhomogeneous Linear Equations .

boundary conditions is called a boundary-value problem (BVP). Boundary con-ditions come in many forms. For example, y(6) = y(22); y0(7) = 3y(0); y(9) = 5 are all examples of boundary conditions. Boundary-value problems, like the one in the example, where the boundary condition consists of specifying the value of the solution at some point are ...

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