2.8.2 First order Frobenius series

Table 2.1259: First order Frobenius series [23]

#

ODE

solved

Maple

Mma

Sympy

time(sec)

414

\begin{align*} x y^{\prime }+y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.267

415

\begin{align*} 2 x y^{\prime }&=y \\ \end{align*}

Series expansion around \(x=0\).

0.268

1056

\begin{align*} x y^{\prime }+y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.260

1057

\begin{align*} 2 x y^{\prime }&=y \\ \end{align*}

Series expansion around \(x=0\).

0.260

7360

\begin{align*} x y^{\prime }&=y x +y \\ \end{align*}

Series expansion around \(x=0\).

0.358

7364

\begin{align*} x y^{\prime }&=y \\ \end{align*}

Series expansion around \(x=0\).

0.265

8568

\begin{align*} x y^{\prime }-3 y&=k \\ \end{align*}

Series expansion around \(x=0\).

0.464

9359

\begin{align*} x y^{\prime }&=y \\ \end{align*}

Series expansion around \(x=0\).

0.519

9363

\begin{align*} y^{\prime }-\frac {y}{x}&=x^{2} \\ \end{align*}

Series expansion around \(x=0\).

0.628

10244

\begin{align*} x y^{\prime }+y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.266

10349

\begin{align*} x y^{\prime }+y&=x \\ \end{align*}

Series expansion around \(x=0\).

0.344

10350

\begin{align*} x y^{\prime }+y&=1 \\ \end{align*}

Series expansion around \(x=0\).

0.339

10351

\begin{align*} x y^{\prime }+y&=\sin \left (x \right ) \\ \end{align*}

Series expansion around \(x=0\).

0.411

10352

\begin{align*} x y^{\prime }+y&=2 x^{4}+x^{3}+x \\ \end{align*}

Series expansion around \(x=0\).

0.393

10353

\begin{align*} x y^{\prime }+y&=\frac {1}{x^{3}} \\ \end{align*}

Series expansion around \(x=0\).

0.328

10354

\begin{align*} x y^{\prime }+2 y x&=\sqrt {x} \\ \end{align*}

Series expansion around \(x=0\).

0.628

10355

\begin{align*} y^{\prime }+\frac {y}{x}&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.286

10356

\begin{align*} \cos \left (x \right ) y^{\prime }+\frac {y}{x}&=x \\ \end{align*}

Series expansion around \(x=0\).

0.694

10357

\begin{align*} \cos \left (x \right ) y^{\prime }+\frac {y}{x}&=x +\sin \left (x \right ) \\ \end{align*}

Series expansion around \(x=0\).

0.973

10358

\begin{align*} x y^{\prime }+y&=\tan \left (x \right ) \\ \end{align*}

Series expansion around \(x=0\).

0.483

10359

\begin{align*} x y^{\prime }+y&=\cos \left (x \right )+\sin \left (x \right ) \\ \end{align*}

Series expansion around \(x=0\).

0.471

19580

\begin{align*} x y^{\prime }&=y \\ \end{align*}

Series expansion around \(x=0\).

0.306

24097

\begin{align*} x y^{\prime }+\left (x +1\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.397