2.2.171 Problems 17001 to 17100

Table 2.355: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

Maple

Mma

Sympy

time(sec)

17001

\begin{align*} y^{\prime }&=4 x^{3}-x +2 \\ y \left (0\right ) &= 1 \\ \end{align*}

[_quadrature]

0.315

17002

\begin{align*} y^{\prime }&=\sin \left (2 t \right )-\cos \left (2 t \right ) \\ y \left (0\right ) &= 0 \\ \end{align*}

[_quadrature]

0.403

17003

\begin{align*} y^{\prime }&=\frac {\cos \left (\frac {1}{x}\right )}{x^{2}} \\ y \left (\frac {2}{\pi }\right ) &= 1 \\ \end{align*}

[_quadrature]

0.467

17004

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

[_quadrature]

0.358

17005

\begin{align*} y^{\prime }&=\frac {\left (x -4\right ) y^{3}}{x^{3} \left (y-2\right )} \\ \end{align*}

[_separable]

6.742

17006

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

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

2.571

17007

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

[_linear]

1.695

17008

\begin{align*} 16 y^{\prime \prime }+24 y^{\prime }+153 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.251

17009

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

system_of_ODEs

0.815

17010

\begin{align*} 4 \left (y^{2}+x^{2}\right ) x -5 y+4 y \left (x^{2}+y^{2}-5 x \right ) y^{\prime }&=0 \\ \end{align*}

[_rational]

22.187

17011

\begin{align*} y^{\prime }&=\sin \left (x \right )^{4} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_quadrature]

0.543

17012

\begin{align*} y^{\prime \prime \prime \prime }+\frac {25 y^{\prime \prime }}{2}-5 y^{\prime }+\frac {629 y}{16}&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ y^{\prime \prime }\left (0\right ) &= -1 \\ y^{\prime \prime \prime }\left (0\right ) &= 1 \\ \end{align*}

[[_high_order, _missing_x]]

0.115

17013

\begin{align*} x^{\prime }&=4 y \\ y^{\prime }&=-4 x \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 4 \\ y \left (0\right ) &= 0 \\ \end{align*}

system_of_ODEs

0.391

17014

\begin{align*} x^{\prime }&=-5 x+4 y \\ y^{\prime }&=2 x+2 y \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 4 \\ y \left (0\right ) &= 0 \\ \end{align*}

system_of_ODEs

0.437

17015

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

[_separable]

2.008

17016

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

[[_linear, ‘class A‘]]

1.524

17017

\begin{align*} y^{\prime \prime }+4 y^{\prime }-5 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.187

17018

\begin{align*} y^{\prime \prime }-6 y^{\prime }+45 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.258

17019

\begin{align*} x^{2} y^{\prime \prime }-y^{\prime } x -16 y&=0 \\ \end{align*}

[[_Emden, _Fowler]]

0.881

17020

\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +2 y&=0 \\ \end{align*}

[[_Emden, _Fowler]]

1.012

17021

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

[[_2nd_order, _with_linear_symmetries]]

0.373

17022

\begin{align*} 12 y-7 y^{\prime }+y^{\prime \prime }&=2 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.295

17023

\begin{align*} 2 x -3 y+\left (-3 x +2 y\right ) y^{\prime }&=0 \\ \end{align*}

[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

4.158

17024

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

[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]

3.001

17025

\begin{align*} y^{\prime }&=x \,{\mathrm e}^{-x^{2}} \\ \end{align*}

[_quadrature]

0.227

17026

\begin{align*} y^{\prime }&=x^{2} \sin \left (x \right ) \\ \end{align*}

[_quadrature]

0.246

17027

\begin{align*} y^{\prime }&=\frac {2 x^{2}-x +1}{\left (x -1\right ) \left (x^{2}+1\right )} \\ \end{align*}

[_quadrature]

0.253

17028

\begin{align*} y^{\prime }&=\frac {x^{2}}{\sqrt {x^{2}-1}} \\ \end{align*}

[_quadrature]

0.283

17029

\begin{align*} 2 y+y^{\prime }&=x^{2} \\ y \left (0\right ) &= 1 \\ \end{align*}

[[_linear, ‘class A‘]]

1.631

17030

\begin{align*} y^{\prime \prime }+4 y&=t \\ y \left (\frac {\pi }{4}\right ) &= 1 \\ y^{\prime }\left (\frac {\pi }{4}\right ) &= \frac {\pi }{16} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

0.517

17031

\begin{align*} x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=0 \\ y \left (1\right ) &= 1 \\ y^{\prime }\left (1\right ) &= 0 \\ \end{align*}

[[_Emden, _Fowler]]

0.997

17032

\begin{align*} y^{\prime }&=\cos \left (x \right )^{2} \sin \left (x \right ) \\ y \left (0\right ) &= 0 \\ \end{align*}

[_quadrature]

0.374

17033

\begin{align*} y^{\prime }&=\frac {4 x -9}{3 \left (x -3\right )^{{2}/{3}}} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_quadrature]

0.408

17034

\begin{align*} y^{\prime }+t^{2}&=y^{2} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_Riccati]

8.667

17035

\begin{align*} y^{\prime }+t^{2}&=\frac {1}{y^{2}} \\ \end{align*}

[_rational]

1.056

17036

\begin{align*} y^{\prime }&=y+\frac {1}{1-t} \\ \end{align*}

[_linear]

1.487

17037

\begin{align*} y^{\prime }&=y^{{1}/{5}} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_quadrature]

2.991

17038

\begin{align*} \frac {y^{\prime }}{t}&=\sqrt {y} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

10.939

17039

\begin{align*} y^{\prime }&=4 t^{2}-t y^{2} \\ y \left (2\right ) &= 1 \\ \end{align*}

[_Riccati]

3.529

17040

\begin{align*} y^{\prime }&=y \sqrt {t} \\ y \left (1\right ) &= 1 \\ \end{align*}

[_separable]

2.411

17041

\begin{align*} y^{\prime }&=6 y^{{2}/{3}} \\ y \left (1\right ) &= 0 \\ \end{align*}

[_quadrature]

1.538

17042

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

[_separable]

1.714

17043

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

[_separable]

2.155

17044

\begin{align*} y^{\prime }&=\frac {1}{t^{2}+1} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_quadrature]

0.306

17045

\begin{align*} y^{\prime }&=\sqrt {y^{2}-1} \\ y \left (0\right ) &= 2 \\ \end{align*}

[_quadrature]

3.807

17046

\begin{align*} y^{\prime }&=\sqrt {y^{2}-1} \\ y \left (4\right ) &= -1 \\ \end{align*}

[_quadrature]

6.632

17047

\begin{align*} y^{\prime }&=\sqrt {y^{2}-1} \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}

[_quadrature]

3.643

17048

\begin{align*} y^{\prime }&=\sqrt {y^{2}-1} \\ y \left (2\right ) &= 1 \\ \end{align*}

[_quadrature]

10.545

17049

\begin{align*} y^{\prime }&=\sqrt {25-y^{2}} \\ y \left (-4\right ) &= 3 \\ \end{align*}

[_quadrature]

27.977

17050

\begin{align*} y^{\prime }&=\sqrt {25-y^{2}} \\ y \left (0\right ) &= 5 \\ \end{align*}

[_quadrature]

1.721

17051

\begin{align*} y^{\prime }&=\sqrt {25-y^{2}} \\ y \left (3\right ) &= -6 \\ \end{align*}

[_quadrature]

4.408

17052

\begin{align*} y^{\prime }&=\sqrt {25-y^{2}} \\ y \left (4\right ) &= -5 \\ \end{align*}

[_quadrature]

35.981

17053

\begin{align*} t y^{\prime }+y&=t^{3} \\ y \left (1\right ) &= 0 \\ \end{align*}

[_linear]

2.570

17054

\begin{align*} t^{3} y^{\prime }+t^{4} y&=2 t^{3} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_linear]

1.421

17055

\begin{align*} 2 y^{\prime }+t y&=\ln \left (t \right ) \\ y \left ({\mathrm e}\right ) &= 0 \\ \end{align*}

[_linear]

2.194

17056

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

[_linear]

2.473

17057

\begin{align*} y^{\prime }+\frac {y}{t -3}&=\frac {1}{-1+t} \\ y \left (-1\right ) &= 0 \\ \end{align*}

[_linear]

2.034

17058

\begin{align*} \left (t -2\right ) y^{\prime }+\left (t^{2}-4\right ) y&=\frac {1}{t +2} \\ y \left (0\right ) &= 3 \\ \end{align*}

[_linear]

2.184

17059

\begin{align*} y^{\prime }+\frac {y}{\sqrt {-t^{2}+4}}&=t \\ y \left (0\right ) &= 0 \\ \end{align*}

[_linear]

3.247

17060

\begin{align*} y^{\prime }+\frac {y}{\sqrt {-t^{2}+4}}&=t \\ y \left (3\right ) &= -1 \\ \end{align*}

[_linear]

3.895

17061

\begin{align*} t y^{\prime }+y&=t \sin \left (t \right ) \\ y \left (\pi \right ) &= 1 \\ \end{align*}

[_linear]

1.823

17062

\begin{align*} \tan \left (t \right ) y+y^{\prime }&=\sin \left (t \right ) \\ y \left (0\right ) &= 0 \\ \end{align*}

[_linear]

3.192

17063

\begin{align*} y^{\prime }&=y^{2} \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}

[_quadrature]

3.530

17064

\begin{align*} y^{\prime }&=t y^{2} \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}

[_separable]

5.286

17065

\begin{align*} y^{\prime }&=-\frac {t}{y} \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}

[_separable]

6.007

17066

\begin{align*} y^{\prime }&=-y^{3} \\ y \left (0\right ) &= {\frac {1}{2}} \\ \end{align*}

[_quadrature]

31.080

17067

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

[_separable]

2.744

17068

\begin{align*} \frac {1}{2 \sqrt {t}}+y^{2} y^{\prime }&=0 \\ \end{align*}

[_separable]

3.059

17069

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

[_separable]

5.461

17070

\begin{align*} y^{\prime }&=\frac {1+y^{2}}{y} \\ \end{align*}

[_quadrature]

0.717

17071

\begin{align*} 6+4 t^{3}+\left (5+\frac {9}{y^{8}}\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

2.504

17072

\begin{align*} \frac {6}{t^{9}}-\frac {6}{t^{3}}+t^{7}+\left (9+\frac {1}{s^{2}}-4 s^{8}\right ) s^{\prime }&=0 \\ \end{align*}

[_separable]

3.023

17073

\begin{align*} 4 \sinh \left (4 y\right ) y^{\prime }&=6 \cosh \left (3 x \right ) \\ \end{align*}

[_separable]

2.798

17074

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

[_separable]

2.115

17075

\begin{align*} y^{\prime }&=\frac {2+y}{2 t +1} \\ \end{align*}

[_separable]

3.580

17076

\begin{align*} \frac {3}{t^{2}}&=\left (\frac {1}{\sqrt {y}}+\sqrt {y}\right ) y^{\prime } \\ \end{align*}

[_separable]

3.383

17077

\begin{align*} 3 \sin \left (x \right )-4 y^{\prime } \cos \left (y\right )&=0 \\ \end{align*}

[_separable]

2.183

17078

\begin{align*} \cos \left (y\right ) y^{\prime }&=8 \sin \left (8 t \right ) \\ \end{align*}

[_separable]

3.087

17079

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

[_quadrature]

0.822

17080

\begin{align*} \left (5 x^{5}-4 \cos \left (x\right )\right ) x^{\prime }+2 \cos \left (9 t \right )+2 \sin \left (7 t \right )&=0 \\ \end{align*}

[_separable]

4.840

17081

\begin{align*} \cosh \left (6 t \right )+5 \sinh \left (4 t \right )+20 \sinh \left (y\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

7.320

17082

\begin{align*} y^{\prime }&={\mathrm e}^{2 y+10 t} \\ \end{align*}

[_separable]

1.685

17083

\begin{align*} y^{\prime }&={\mathrm e}^{3 y+2 t} \\ \end{align*}

[_separable]

1.709

17084

\begin{align*} \sin \left (t \right )^{2}&=\cos \left (y\right )^{2} y^{\prime } \\ \end{align*}

[_separable]

2.729

17085

\begin{align*} 3 \sin \left (t \right )-\sin \left (3 t \right )&=\left (\cos \left (4 y\right )-4 \cos \left (y\right )\right ) y^{\prime } \\ \end{align*}

[_separable]

28.892

17086

\begin{align*} x^{\prime }&=\frac {\sec \left (t \right )^{2}}{\sec \left (x\right ) \tan \left (x\right )} \\ \end{align*}

[_separable]

27.240

17087

\begin{align*} \left (2-\frac {5}{y^{2}}\right ) y^{\prime }+4 \cos \left (x \right )^{2}&=0 \\ \end{align*}

[_separable]

2.927

17088

\begin{align*} y^{\prime }&=\frac {t^{3}}{y \sqrt {\left (1-y^{2}\right ) \left (t^{4}+9\right )}} \\ \end{align*}

[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]

5.744

17089

\begin{align*} \tan \left (y\right ) \sec \left (y\right )^{2} y^{\prime }+\cos \left (2 x \right )^{3} \sin \left (2 x \right )&=0 \\ \end{align*}

[_separable]

3.690

17090

\begin{align*} y^{\prime }&=\frac {\left (1+2 \,{\mathrm e}^{y}\right ) {\mathrm e}^{-y}}{t \ln \left (t \right )} \\ \end{align*}

[_separable]

3.566

17091

\begin{align*} x \sin \left (x^{2}\right )&=\frac {\cos \left (\sqrt {y}\right ) y^{\prime }}{\sqrt {y}} \\ \end{align*}

[_separable]

9.737

17092

\begin{align*} \frac {x -2}{x^{2}-4 x +3}&=\frac {\left (1-\frac {1}{y}\right )^{2} y^{\prime }}{y^{2}} \\ \end{align*}

[_separable]

3.257

17093

\begin{align*} \frac {\cos \left (y\right ) y^{\prime }}{\left (1-\sin \left (y\right )\right )^{2}}&=\sin \left (x \right )^{3} \cos \left (x \right ) \\ \end{align*}

[_separable]

10.355

17094

\begin{align*} y^{\prime }&=\frac {\left (5-2 \cos \left (x \right )\right )^{3} \sin \left (x \right ) \cos \left (y\right )^{4}}{\sin \left (y\right )} \\ \end{align*}

[_separable]

13.269

17095

\begin{align*} \frac {\sqrt {\ln \left (x \right )}}{x}&=\frac {{\mathrm e}^{\frac {3}{y}} y^{\prime }}{y} \\ \end{align*}

[_separable]

2.375

17096

\begin{align*} y^{\prime }&=\frac {5^{-t}}{y^{2}} \\ \end{align*}

[_separable]

1.822

17097

\begin{align*} y^{\prime }&=t^{2} y^{2}+y^{2}-t^{2}-1 \\ \end{align*}

[_separable]

3.358

17098

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

[_quadrature]

0.507

17099

\begin{align*} 4 \left (x -1\right )^{2} y^{\prime }-3 \left (3+y\right )^{2}&=0 \\ \end{align*}

[_separable]

4.398

17100

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

[_separable]

4.799