Collection of transformations

3.15.2 Collection of transformations

3.15.2.1 Example \(x^{2}y^{\prime \prime }+xy^{\prime }+\left ( ax^{2}-n^{2}\right ) y=0\)
3.15.2.2 Example \(x^{2}y^{\prime \prime }+xy^{\prime }+xy=0\)
3.15.2.3 Example \(x^{2}y^{\prime \prime }+bxy^{\prime }+\left ( x^{2}-v^{2}\right ) y=0\)
3.15.2.4 Example \(xy^{\prime \prime }+y^{\prime }+Ay=0\)
3.15.2.5 Example \(y^{\prime \prime }-\frac {1}{x}y=0\)
3.15.2.6 Example \(4x^{2}y^{\prime \prime }+4xy^{\prime }+\left ( x-4\right ) y=0\)
3.15.2.7 Example \(y^{\prime \prime }-\frac {1}{x^{\frac {3}{2}}}y=0\)
3.15.2.8 Example \(x^{2}y^{\prime \prime }-xy+\left ( x^{2}+1\right ) y=0\)
3.15.2.9 Example \(y^{\prime \prime }-x^{-\frac {1}{4}}y=0\)
3.15.2.10 Example \(f^{\prime \prime }+\frac {\lambda }{x}f^{\prime }-\mu f=0\)
3.15.2.11 Example \(x^{2}y^{\prime \prime }+xy^{\prime }+(x^{2}-5)y=0\)

This section shows number of transformations applied to second order linear ode in order to make it of the form (A) or (B) if it is not already in that form. Once the ode is in form A or B, then its solution is now known using Bowman transformation.

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