First order Frobenius series

2.8.2 First order Frobenius series

Table 2.1183: First order Frobenius series [23]


#	ODE	solved	Maple	Mma	Sympy	time(sec)

414	\begin{align} y^{\prime } x +y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.171

415	\begin{align} 2 y^{\prime } x&=y \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.175

1056	\begin{align} y^{\prime } x +y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.208

1057	\begin{align} 2 y^{\prime } x&=y \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.217

7360	\begin{align} y^{\prime } x&=y x +y \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.653

7364	\begin{align} y^{\prime } x&=y \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.502

8568	\begin{align} y^{\prime } x -3 y&=k \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.269

9359	\begin{align} y^{\prime } x&=y \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.313

9363	\begin{align} y^{\prime }-\frac {y}{x}&=x^{2} \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.381

10244	\begin{align} y^{\prime } x +y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.402

10349	\begin{align} y^{\prime } x +y&=x \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.500

10350	\begin{align} y^{\prime } x +y&=1 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.492

10351	\begin{align} y^{\prime } x +y&=\sin \left (x \right ) \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.582

10352	\begin{align} y^{\prime } x +y&=2 x^{4}+x^{3}+x \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.552

10353	\begin{align} y^{\prime } x +y&=\frac {1}{x^{3}} \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.447

10354	\begin{align} y^{\prime } x +2 y x&=\sqrt {x} \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.813

10355	\begin{align} y^{\prime }+\frac {y}{x}&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.406

10356	\begin{align} \cos \left (x \right ) y^{\prime }+\frac {y}{x}&=x \\ \end{align} Series expansion around \(x=0\).	✓	✓	✗	✗	0.882

10357	\begin{align} \cos \left (x \right ) y^{\prime }+\frac {y}{x}&=x +\sin \left (x \right ) \\ \end{align} Series expansion around \(x=0\).	✓	✓	✗	✗	1.158

10358	\begin{align} y^{\prime } x +y&=\tan \left (x \right ) \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.653

10359	\begin{align} y^{\prime } x +y&=\cos \left (x \right )+\sin \left (x \right ) \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.626

19580	\begin{align} y^{\prime } x&=y \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.472

24097	\begin{align} y^{\prime } x +\left (x +1\right ) y&=0 \\ \end{align} Series expansion around \(x=0\).	✓	✓	✓	✗	0.319

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