2.2.187 Problems 18601 to 18700

Table 2.387: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

Maple

Mma

Sympy

time(sec)

18601

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

[[_homogeneous, ‘class A‘], _dAlembert]

14.924

18602

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

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

9.738

18603

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

[[_homogeneous, ‘class A‘], _dAlembert]

5.261

18604

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

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

5.253

18605

\begin{align*} y^{\prime }&=\frac {x +y}{x -y} \\ y \left (5\right ) &= 8 \\ \end{align*}

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

78.362

18606

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

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

2.043

18607

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

[_Bernoulli]

1.812

18608

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

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

2.418

18609

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

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

6.944

18610

\begin{align*} 5 \left (t^{2}+1\right ) y^{\prime }&=4 t y \left (y^{3}-1\right ) \\ \end{align*}

[_separable]

31.163

18611

\begin{align*} 3 t y^{\prime }+9 y&=2 t y^{{5}/{3}} \\ \end{align*}

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

31.275

18612

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

[_quadrature]

0.727

18613

\begin{align*} y^{\prime }&=r y-k^{2} y^{2} \\ \end{align*}

[_quadrature]

2.225

18614

\begin{align*} y^{\prime }&=a y+b y^{3} \\ \end{align*}

[_quadrature]

5.234

18615

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

[_Riccati]

2.541

18616

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

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

6.722

18617

\begin{align*} 1&=\left (3 \,{\mathrm e}^{y}-2 x \right ) y^{\prime } \\ \end{align*}

[[_1st_order, _with_exponential_symmetries]]

1.866

18618

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

[[_1st_order, _with_linear_symmetries], _Bernoulli]

1.542

18619

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

[_linear]

1.584

18620

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

[_Bernoulli]

34.780

18621

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

[_separable]

2.159

18622

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

[_separable]

0.084

18623

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

[_exact, _Bernoulli]

2.303

18624

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

[_linear]

2.970

18625

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

[_quadrature]

0.235

18626

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

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

5.309

18627

\begin{align*} 4 x y^{\prime } y&=8 x^{2}+5 y^{2} \\ \end{align*}

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

6.772

18628

\begin{align*} y^{\prime }+y-y^{{1}/{4}}&=0 \\ \end{align*}

[_quadrature]

2.415

18629

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

system_of_ODEs

0.791

18630

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

system_of_ODEs

1.452

18631

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

system_of_ODEs

0.029

18632

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

system_of_ODEs

0.909

18633

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

system_of_ODEs

1.007

18634

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

system_of_ODEs

0.028

18635

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

system_of_ODEs

0.024

18636

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

system_of_ODEs

0.349

18637

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

system_of_ODEs

0.323

18638

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

system_of_ODEs

0.335

18639

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

system_of_ODEs

0.992

18640

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

system_of_ODEs

0.879

18641

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

system_of_ODEs

1.054

18642

\begin{align*} x^{\prime }&=-x-4 y-4 \\ y^{\prime }&=x-y-6 \\ \end{align*}

system_of_ODEs

0.945

18643

\begin{align*} x^{\prime }&=-\frac {x}{4}-\frac {3 y}{4}+8 \\ y^{\prime }&=\frac {x}{2}+y-\frac {23}{2} \\ \end{align*}

system_of_ODEs

1.113

18644

\begin{align*} x^{\prime }&=-2 x+y-11 \\ y^{\prime }&=-5 x+4 y-35 \\ \end{align*}

system_of_ODEs

0.979

18645

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

system_of_ODEs

0.933

18646

\begin{align*} x^{\prime }&=-5 x+4 y-35 \\ y^{\prime }&=-2 x+y-11 \\ \end{align*}

system_of_ODEs

1.023

18647

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

system_of_ODEs

0.347

18648

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

system_of_ODEs

0.330

18649

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

system_of_ODEs

0.354

18650

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

system_of_ODEs

0.341

18651

\begin{align*} x^{\prime }&=4 x-3 y \\ y^{\prime }&=8 x-6 y \\ \end{align*}

system_of_ODEs

0.314

18652

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

system_of_ODEs

0.291

18653

\begin{align*} x^{\prime }&=\frac {5 x}{4}+\frac {3 y}{4} \\ y^{\prime }&=\frac {3 x}{4}+\frac {5 y}{4} \\ \end{align*}

system_of_ODEs

0.314

18654

\begin{align*} x^{\prime }&=-\frac {3 x}{4}-\frac {7 y}{4} \\ y^{\prime }&=\frac {x}{4}+\frac {5 y}{4} \\ \end{align*}

system_of_ODEs

0.347

18655

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

system_of_ODEs

0.328

18656

\begin{align*} x^{\prime }&=5 x-y \\ y^{\prime }&=3 x+y \\ \end{align*}

system_of_ODEs

0.333

18657

\begin{align*} x^{\prime }&=-2 x+y \\ y^{\prime }&=-5 x+4 y \\ \end{align*}

system_of_ODEs

0.325

18658

\begin{align*} x^{\prime }&=3 x+6 y \\ y^{\prime }&=-x-2 y \\ \end{align*}

system_of_ODEs

0.294

18659

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

system_of_ODEs

0.368

18660

\begin{align*} x^{\prime }&=2 x-y \\ y^{\prime }&=3 x-2 y \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 2 \\ y \left (0\right ) &= 5 \\ \end{align*}

system_of_ODEs

0.355

18661

\begin{align*} x^{\prime }&=5 x-y \\ y^{\prime }&=3 x+y \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 2 \\ y \left (0\right ) &= -1 \\ \end{align*}

system_of_ODEs

0.359

18662

\begin{align*} x^{\prime }&=-2 x+y \\ y^{\prime }&=-5 x+4 y \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 3 \\ \end{align*}

system_of_ODEs

0.341

18663

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

system_of_ODEs

0.845

18664

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

system_of_ODEs

0.367

18665

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

system_of_ODEs

0.377

18666

\begin{align*} x^{\prime }&=2 x-\frac {5 y}{2} \\ y^{\prime }&=\frac {9 x}{5}-y \\ \end{align*}

system_of_ODEs

0.526

18667

\begin{align*} x^{\prime }&=x-y \\ y^{\prime }&=5 x-3 y \\ \end{align*}

system_of_ODEs

0.497

18668

\begin{align*} x^{\prime }&=x+2 y \\ y^{\prime }&=-5 x-y \\ \end{align*}

system_of_ODEs

0.400

18669

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

system_of_ODEs

0.382

18670

\begin{align*} x^{\prime }&=2 x-5 y \\ y^{\prime }&=x-2 y \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 3 \\ y \left (0\right ) &= 2 \\ \end{align*}

system_of_ODEs

0.350

18671

\begin{align*} x^{\prime }&=x-5 y \\ y^{\prime }&=x-3 y \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= 1 \\ \end{align*}

system_of_ODEs

0.450

18672

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

system_of_ODEs

0.497

18673

\begin{align*} x^{\prime }&=\frac {3 x}{4}-2 y \\ y^{\prime }&=x-\frac {5 y}{4} \\ \end{align*}

system_of_ODEs

0.459

18674

\begin{align*} x^{\prime }&=-\frac {4 x}{5}+2 y \\ y^{\prime }&=-x+\frac {6 y}{5} \\ \end{align*}

system_of_ODEs

0.461

18675

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

system_of_ODEs

0.337

18676

\begin{align*} x^{\prime }&=-5 y \\ y^{\prime }&=x+a y \\ \end{align*}

system_of_ODEs

0.608

18677

\begin{align*} x^{\prime }&=2 x-5 y \\ y^{\prime }&=a x-2 y \\ \end{align*}

system_of_ODEs

0.492

18678

\begin{align*} x^{\prime }&=\frac {5 x}{4}+\frac {3 y}{4} \\ y^{\prime }&=a x+\frac {5 y}{4} \\ \end{align*}

system_of_ODEs

0.496

18679

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

system_of_ODEs

0.424

18680

\begin{align*} x^{\prime }&=3 x+a y \\ y^{\prime }&=-6 x-4 y \\ \end{align*}

system_of_ODEs

0.538

18681

\begin{align*} x^{\prime }&=a x+10 y \\ y^{\prime }&=-x-4 y \\ \end{align*}

system_of_ODEs

0.679

18682

\begin{align*} x^{\prime }&=4 x+a y \\ y^{\prime }&=8 x-6 y \\ \end{align*}

system_of_ODEs

0.524

18683

\begin{align*} i^{\prime }&=\frac {i}{2}-\frac {v}{8} \\ v^{\prime }&=2 i-\frac {v}{2} \\ \end{align*}

system_of_ODEs

0.259

18684

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

system_of_ODEs

0.278

18685

\begin{align*} x^{\prime }&=\frac {5 x}{4}+\frac {3 y}{4} \\ y^{\prime }&=-\frac {3 x}{4}-\frac {y}{4} \\ \end{align*}

system_of_ODEs

0.291

18686

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

system_of_ODEs

0.300

18687

\begin{align*} x^{\prime }&=-3 x+\frac {5 y}{2} \\ y^{\prime }&=-\frac {5 x}{2}+2 y \\ \end{align*}

system_of_ODEs

0.299

18688

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

system_of_ODEs

0.298

18689

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

system_of_ODEs

0.296

18690

\begin{align*} x^{\prime }&=x-4 y \\ y^{\prime }&=4 x-7 y \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 3 \\ y \left (0\right ) &= 2 \\ \end{align*}

system_of_ODEs

0.335

18691

\begin{align*} x^{\prime }&=-\frac {5 x}{2}+\frac {3 y}{2} \\ y^{\prime }&=-\frac {3 x}{2}+\frac {y}{2} \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 3 \\ y \left (0\right ) &= -1 \\ \end{align*}

system_of_ODEs

0.334

18692

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

system_of_ODEs

0.339

18693

\begin{align*} x^{\prime }&=\frac {5 x}{4}+\frac {3 y}{4} \\ y^{\prime }&=-\frac {3 x}{4}-\frac {y}{4} \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 2 \\ y \left (0\right ) &= 3 \\ \end{align*}

system_of_ODEs

0.331

18694

\begin{align*} x^{\prime }&=-3 x+\frac {5 y}{2} \\ y^{\prime }&=-\frac {5 x}{2}+2 y \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 3 \\ y \left (0\right ) &= 1 \\ \end{align*}

system_of_ODEs

0.322

18695

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

system_of_ODEs

0.320

18696

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

system_of_ODEs

0.311

18697

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

system_of_ODEs

0.304

18698

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

system_of_ODEs

0.303

18699

\begin{align*} x^{\prime }&=2 y \\ y^{\prime }&=8 x \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 2 \\ y \left (0\right ) &= -1 \\ \end{align*}

system_of_ODEs

0.366

18700

\begin{align*} x^{\prime }&=2 y \\ y^{\prime }&=8 x \\ \end{align*}
With initial conditions
\begin{align*} x \left (0\right ) &= 1 \\ y \left (0\right ) &= -3 \\ \end{align*}

system_of_ODEs

0.354