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1
Frobenius series. Indicial equation with repeated root
1.1
Example 1. homogeneous ode
\(x^{2}y^{\prime \prime }\left ( x\right ) +xy^{\prime }\left ( x\right ) +x^{2}y\left ( x\right ) =0\)
1.2
Example 2. inhomogeneous ode example
\(x^{2}y^{\prime \prime }\left ( x\right ) +xy^{\prime }\left ( x\right ) +x^{2}y\left ( x\right ) =\sin \left ( x\right ) \)
1.3
Example 3. homogeneous ode example
\(\left ( e^{x}-1\right ) y^{\prime \prime }\left ( x\right ) +e^{x}y^{\prime }\left ( x\right ) +y\left ( x\right ) =0\)
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