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2
Frobenius series where indicial equation roots differ by an integer
2.1
Example 1. homogeneous ode where log term is needed
\(x^{2}y^{\prime \prime }\left ( x\right ) -xy\left ( x\right ) =0\)
2.2
Example 2. homogeneous ode where log term is needed
\(x^{\frac {3}{2}}y^{\prime \prime }+y=0\)
2.3
Example 3. homogeneous ode where log term is not needed
\(x^{2}y^{\prime \prime }+3xy^{\prime }+4x^{4}y=0\)
2.4
Example 4 inhomogeneous ode example where log term is needed
\(xy^{\prime \prime }+y=x\)
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