2.2.171 Problems 17001 to 17100

Table 2.359: 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]

0.513

17002

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

[_quadrature]

0.645

17003

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

[_quadrature]

0.724

17004

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

[_quadrature]

0.648

17005

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

[_separable]

12.125

17006

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

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

7.597

17007

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

[_linear]

2.360

17008

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

[[_2nd_order, _missing_x]]

0.362

17009

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

system_of_ODEs

1.276

17010

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

[_rational]

60.570

17011

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

[_quadrature]

0.818

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]]

0.138

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

0.478

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

0.531

17015

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

[_separable]

3.694

17016

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

[[_linear, ‘class A‘]]

2.215

17017

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

[[_2nd_order, _missing_x]]

0.284

17018

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

[[_2nd_order, _missing_x]]

0.349

17019

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

[[_Emden, _Fowler]]

1.447

17020

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

[[_Emden, _Fowler]]

2.147

17021

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

[[_2nd_order, _with_linear_symmetries]]

0.721

17022

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

[[_2nd_order, _missing_x]]

0.424

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‘]]

21.208

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)]‘]]

4.111

17025

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

[_quadrature]

0.365

17026

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

[_quadrature]

0.531

17027

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

[_quadrature]

0.523

17028

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

[_quadrature]

0.629

17029

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

[[_linear, ‘class A‘]]

2.917

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]]

0.684

17031

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

[[_Emden, _Fowler]]

1.699

17032

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

[_quadrature]

0.534

17033

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

[_quadrature]

0.674

17034

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

[_Riccati]

8.862

17035

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

[_rational]

13.817

17036

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

[_linear]

2.108

17037

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

[_quadrature]

48.957

17038

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

[_separable]

35.115

17039

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

[_Riccati]

6.548

17040

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

[_separable]

4.573

17041

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

[_quadrature]

2.917

17042

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

[_separable]

3.196

17043

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

[_separable]

4.652

17044

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

[_quadrature]

0.450

17045

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

[_quadrature]

23.329

17046

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

[_quadrature]

15.518

17047

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

[_quadrature]

16.987

17048

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

[_quadrature]

15.845

17049

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

[_quadrature]

355.482

17050

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

[_quadrature]

10.347

17051

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

[_quadrature]

81.023

17052

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

[_quadrature]

86.464

17053

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

[_linear]

5.173

17054

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

[_linear]

2.234

17055

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

[_linear]

3.732

17056

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

[_linear]

3.243

17057

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

[_linear]

2.821

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]

3.842

17059

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

[_linear]

5.964

17060

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

[_linear]

5.776

17061

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

[_linear]

2.571

17062

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

[_linear]

3.175

17063

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

[_quadrature]

4.189

17064

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

[_separable]

10.471

17065

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

[_separable]

41.807

17066

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

[_quadrature]

26.314

17067

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

[_separable]

6.146

17068

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

[_separable]

8.683

17069

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

[_separable]

15.724

17070

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

[_quadrature]

1.356

17071

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

[_separable]

4.144

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]

4.975

17073

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

[_separable]

5.601

17074

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

[_separable]

3.832

17075

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

[_separable]

10.402

17076

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

[_separable]

6.062

17077

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

[_separable]

3.292

17078

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

[_separable]

5.421

17079

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

[_quadrature]

1.998

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]

7.301

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]

8.209

17082

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

[_separable]

3.556

17083

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

[_separable]

3.493

17084

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

[_separable]

4.002

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]

27.938

17086

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

[_separable]

26.936

17087

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

[_separable]

5.040

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)]‘]]

7.993

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]

5.998

17090

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

[_separable]

7.322

17091

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

[_separable]

14.462

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]

5.234

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]

11.573

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]

13.776

17095

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

[_separable]

3.701

17096

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

[_separable]

3.757

17097

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

[_separable]

6.022

17098

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

[_quadrature]

1.154

17099

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

[_separable]

9.948

17100

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

[_separable]

9.782