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3
Frobenius series. Indicial equation with root that differ by non integer
3.1
Example 1. homogeneous ode
\(2x^{2}y^{\prime \prime }\left ( x\right ) -xy^{\prime }\left ( x\right ) +\left ( 1-x^{2}\right ) y\left ( x\right ) =0\)
3.2
Example 2. homogeneous ode
\(2x^{2}y^{\prime \prime }\left ( x\right ) -xy^{\prime }\left ( x\right ) +\left ( 1-x^{2}\right ) y\left ( x\right ) =1+x\)
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