Engng Math 145 Differential Equations

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4 Terms

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Seperable differential equations & solving

  1. Put ouput variable on LHS and input on RHS

  2. Times both side by dx and integrate (only RHS gets +C)

  3. Make output variable subject of equation if possible

<ol><li><p>Put ouput variable on LHS and input on RHS</p></li><li><p>Times both side by dx and integrate (only RHS gets +C)</p></li><li><p>Make output variable subject of equation if possible</p></li></ol><p></p>
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Linear differential equations & solving

  1. Calculate I(x) = e∫P(x)dx (integrating factor)

  2. [Multiply boths sides by I(x)]

  3. Then: y = (1 / I(x)) * ∫ I(x) Q(x) dx

When calculating e∫P(x)dx no +C needed.

<ol><li><p>Calculate I(x) = e<sup>∫P(x)dx</sup> (integrating factor)</p></li><li><p>[Multiply boths sides by I(x)]</p></li><li><p>Then: y = (1 / I(x)) * ∫ I(x) Q(x) dx</p></li></ol><p>When calculating e<sup>∫P(x)dx</sup> no +C needed.</p>
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Word differential equations

  1. Form LDE: eg. dy/dt = rate in - rate out → eg. dy/dt = input conc. decimal * rate1 - (y / (room volume)) * rate2

  2. Solve LDE.

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Differential equation notes

  • y’ = dy/dx & y’’ = d2y/dx2

  • “Initial value” is just values that should be used to find C.

  • For “solutions”, input into DE and see if equivalent.