Quiz 1 Study Guide

Quiz 1 Study Guide - Form Step 1 Find the partial...

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Differential Equations: Quiz 1 Study Guide § 2.1 – First Order Linear Equations Form: Step 1 : Find integrating factor The integrating factor is , where Step 2 : Multiply by the integrating factor then rewrite the function as Step 3 : Integrate both sides then add the constant of integration. Then isolate to find the general solution. If given initial conditions, solve for C. § 2.2 – Separable Equations Form: Step 1 : Write out the equation so that x and y appear separately Step 2 : Integrate with respect to x, Step 3 : If given initial conditions, use to find the constant of integration and rewrite the final equation. § 2.5 – Logistic Model I DON’T KNOW WHAT TO DO HERE!! § 2.6 – Exact Equations
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Unformatted text preview: Form: Step 1 : Find the partial derivative M in terms of y (M y ) and N in terms of x (N x ) Step 2 : If M y and N x are equal, then proceed to solve for Ψ Step 3 : Setup the system of equations such that: , where the solution Step 4 : Integrate such that , where y is a constant. At the end, the constant is a function of y, so add C(y) Step 5 : Differentiate in respect to y such that , where the solution ends with . Step 6 : Set from the original equation equal to each other and solve for Step 7 : Write out the final solution of including and solve for C if given initial conditions. § 2.7 – Euler Method Goal : To find an approximate solution numerically Given : Form :...
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Quiz 1 Study Guide - Form Step 1 Find the partial...

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