2.2.8 Problems 701 to 800

Table 2.29: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

Maple

Mma

Sympy

time(sec)

701

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

[_separable]

2.895

702

\begin{align*} y^{\prime }&=6 \,{\mathrm e}^{2 x -y} \\ y \left (0\right ) &= 0 \\ \end{align*}

[_separable]

2.120

703

\begin{align*} 2 \sqrt {x}\, y^{\prime }&=\cos \left (y\right )^{2} \\ y \left (4\right ) &= \frac {\pi }{4} \\ \end{align*}

[_separable]

2.790

704

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

[_quadrature]

0.521

705

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

[[_linear, ‘class A‘]]

1.273

706

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

[[_linear, ‘class A‘]]

2.856

707

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

[_linear]

2.615

708

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

[_linear]

3.587

709

\begin{align*} 2 y^{\prime } x +y&=10 \sqrt {x} \\ y \left (2\right ) &= 5 \\ \end{align*}

[_linear]

1.981

710

\begin{align*} 2 y^{\prime } x +y&=10 \sqrt {x} \\ \end{align*}

[_linear]

1.230

711

\begin{align*} y+3 y^{\prime } x&=12 x \\ \end{align*}

[_linear]

2.887

712

\begin{align*} -y+y^{\prime } x&=x \\ y \left (1\right ) &= 7 \\ \end{align*}

[_linear]

2.635

713

\begin{align*} 2 y^{\prime } x -3 y&=9 x^{3} \\ \end{align*}

[_linear]

2.512

714

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

[_separable]

1.960

715

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

[_linear]

2.997

716

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

[[_linear, ‘class A‘]]

1.258

717

\begin{align*} y^{\prime } x -3 y&=x^{3} \\ y \left (1\right ) &= 10 \\ \end{align*}

[_linear]

2.177

718

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

[_separable]

2.041

719

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

[_separable]

3.537

720

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

[_linear]

2.328

721

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

[_linear]

3.063

722

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

[_linear]

2.286

723

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

[_separable]

2.196

724

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

[_linear]

4.156

725

\begin{align*} y^{\prime }&=2 y x +3 x^{2} {\mathrm e}^{x^{2}} \\ y \left (0\right ) &= 5 \\ \end{align*}

[_linear]

4.079

726

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

[_linear]

1.039

727

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

[_separable]

2.878

728

\begin{align*} \left (x^{2}+1\right ) y^{\prime }+3 x^{3} y&=6 x \,{\mathrm e}^{-\frac {3 x^{2}}{2}} \\ y \left (0\right ) &= 1 \\ \end{align*}

[_linear]

2.839

729

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

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

4.433

730

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

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

5.165

731

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

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

4.125

732

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

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

3.745

733

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

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

4.330

734

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

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

3.987

735

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

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

4.567

736

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

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

3.191

737

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

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

2.198

738

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

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

4.296

739

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

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

3.131

740

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

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

7.845

741

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

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

3.818

742

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

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

3.870

743

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

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

4.401

744

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

[[_homogeneous, ‘class C‘], _dAlembert]

1.504

745

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

[[_homogeneous, ‘class C‘], _Riccati]

1.057

746

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

[_quadrature]

0.089

747

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

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

3.984

748

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

[_separable]

1.650

749

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

[_quadrature]

0.789

750

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

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

2.686

751

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

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

10.001

752

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

[_Bernoulli]

2.967

753

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

[_Bernoulli]

9.540

754

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

[[_1st_order, _with_linear_symmetries], _Bernoulli]

1.165

755

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

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

2.178

756

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

[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]]

1.730

757

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

[‘y=_G(x,y’)‘]

2.955

758

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

[[_1st_order, _with_linear_symmetries]]

1.971

759

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

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

3.332

760

\begin{align*} 4 x -y+\left (6 y-x \right ) y^{\prime }&=0 \\ \end{align*}

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

3.289

761

\begin{align*} 3 x^{2}+2 y^{2}+\left (4 y x +6 y^{2}\right ) y^{\prime }&=0 \\ \end{align*}

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

6.542

762

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

[_exact, _rational]

1.704

763

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

[_exact]

1.776

764

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

[_exact]

23.292

765

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

[_exact]

3.063

766

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

[_exact]

2.073

767

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

[_exact, _rational]

0.258

768

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

[_exact]

9.395

769

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

[_exact, _rational]

9.991

770

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

[[_1st_order, _with_linear_symmetries], _exact, _rational]

2.186

771

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

[_linear]

1.441

772

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

[_separable]

1.987

773

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

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

2.275

774

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

[_exact]

2.523

775

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

[_separable]

1.929

776

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

[_separable]

2.016

777

\begin{align*} 2 x^{2} y+x^{3} y^{\prime }&=1 \\ \end{align*}

[_linear]

1.526

778

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

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

3.824

779

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

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

3.967

780

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

[_separable]

2.441

781

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

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

2.386

782

\begin{align*} 6 x y^{3}+2 y^{4}+\left (9 y^{2} x^{2}+8 x y^{3}\right ) y^{\prime }&=0 \\ \end{align*}

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

0.242

783

\begin{align*} y^{\prime }&=1+x^{2}+y^{2}+x^{2} y^{4} \\ \end{align*}

[‘y=_G(x,y’)‘]

0.878

784

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

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

54.609

785

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

[[_linear, ‘class A‘]]

2.170

786

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

[[_homogeneous, ‘class C‘], _Riccati]

1.062

787

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

[_exact]

2.858

788

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

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

58.489

789

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

[_separable]

2.013

790

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

[_linear]

2.331

791

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

[_linear]

1.385

792

\begin{align*} y^{\prime } x&=6 y+12 x^{4} y^{{2}/{3}} \\ \end{align*}

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

6.505

793

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

[_exact]

26.871

794

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

[_separable]

2.504

795

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

[_linear]

2.078

796

\begin{align*} 9 \sqrt {x}\, y^{{4}/{3}}-12 x^{{1}/{5}} y^{{3}/{2}}+\left (8 x^{{3}/{2}} y^{{1}/{3}}-15 x^{{6}/{5}} \sqrt {y}\right ) y^{\prime }&=0 \\ \end{align*}

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

0.191

797

\begin{align*} 3 y+y^{4} x^{3}+3 y^{\prime } x&=0 \\ \end{align*}

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

2.095

798

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

[_linear]

1.454

799

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

[_linear]

5.198

800

\begin{align*} y^{\prime }&=3 \left (y+7\right ) x^{2} \\ \end{align*}

[_separable]

1.589