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3.6.6 Solving Equations Involving Power Series
Solving equations involving power series.
Here is a power series.
In[1]:= y = 1 + Sum[a[i] x^i, {i, 3}] + O[x]^4
Out[1]= 
This gives an equation involving the power series.
In[2]:= D[y, x]^2 - y == x
Out[2]= 
LogicalExpand generates a sequence of equations for each power of x.
In[3]:= LogicalExpand[ % ]
Out[3]= 
This solves the equations for the coefficients a[i]. You can also feed equations involving power series directly to Solve.
In[4]:= Solve[ % ]
Out[4]= 
Some equations involving power series can also be solved using the InverseSeries function discussed in Section 3.6.4.
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