Chem Differential Eq HW Solutions Fall 2011 195

Chem Differential Eq HW Solutions Fall 2011 195 - Out[85]=...

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Section A.5 The Power Series Method, Part II A195 The following notebook illustrates how we can use Mathematica to solve a differential equations with poser series. The solution is y and we will solve for the first 10 coefficients. Let's define a partial sum of the Taylor series solution (degree 3) and set y[0]=1: In[82]:= seriessol Series y x , x, 0, 3 .y 0 1 Out[82]= 1 y 0 x 1 2 y 0 x 2 1 6 y 3 0 x 3 O x 4 Next we set equations based on the given differential equation y'+y=0. In[83]:= leftside D seriessol, x seriessol rightside 0 equat LogicalExpand leftside rightside Out[83]= 1 y 0 y 0 y 0 x y 0 2 1 2 y 3 0 x 2 O x 3 Out[84]=
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Unformatted text preview: Out[85]= 1 y 0 && y y 0 && y 2 1 2 y 3 This gives you a set of equations in the coefficients that Mathematica can solve In[86]:= seriescoeff Solve equat Out[86]= y 1, y 1, y 3 1 Next, we substitute these coefficients in the series solution. This can be done as follows In[87]:= seriessol . seriescoeff 1 Out[87]= 1 x x 2 2 x 3 6 O x 4 To get a partial sum without the Big O, use In[88]:= Normal seriessol . seriescoeff 1 Out[88]= 1 x x 2 2 x 3 6...
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