2.2.48 Problems 4701 to 4800

Table 2.97: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

4701

\[ {}y^{\prime } = a +b y+\sqrt {\operatorname {A0} +\operatorname {B0} y} \]

[_quadrature]

78.381

4702

\[ {}y^{\prime } = a x +b \sqrt {y} \]

[[_homogeneous, ‘class G‘], _Chini]

4.493

4703

\[ {}y^{\prime }+x^{3} = x \sqrt {x^{4}+4 y} \]

[[_1st_order, _with_linear_symmetries]]

3.899

4704

\[ {}y^{\prime }+2 y \left (1-x \sqrt {y}\right ) = 0 \]

[_Bernoulli]

1.306

4705

\[ {}y^{\prime } = \sqrt {a +b y^{2}} \]

[_quadrature]

8.455

4706

\[ {}y^{\prime } = y \sqrt {a +b y} \]

[_quadrature]

119.475

4707

\[ {}y^{\prime }+\left (f \left (x \right )-y\right ) g \left (x \right ) \sqrt {\left (y-a \right ) \left (y-b \right )} = 0 \]

[‘y=_G(x,y’)‘]

5.625

4708

\[ {}y^{\prime } = \sqrt {X Y} \]

[_quadrature]

0.437

4709

\[ {}y^{\prime } = \cos \left (x \right )^{2} \cos \left (y\right ) \]

[_separable]

2.479

4710

\[ {}y^{\prime } = \sec \left (x \right )^{2} \cot \left (y\right ) \cos \left (y\right ) \]

[_separable]

2.897

4711

\[ {}y^{\prime } = a +b \cos \left (A x +B y\right ) \]

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

36.640

4712

\[ {}y^{\prime }+f \left (x \right )+g \left (x \right ) \sin \left (a y\right )+h \left (x \right ) \cos \left (a y\right ) = 0 \]

[‘y=_G(x,y’)‘]

6.354

4713

\[ {}y^{\prime } = a +b \cos \left (y\right ) \]

[_quadrature]

37.933

4714

\[ {}y^{\prime }+x \left (\sin \left (2 y\right )-x^{2} \cos \left (y\right )^{2}\right ) = 0 \]

[‘y=_G(x,y’)‘]

5.098

4715

\[ {}y^{\prime }+\tan \left (x \right ) \sec \left (x \right ) \cos \left (y\right )^{2} = 0 \]

[_separable]

2.635

4716

\[ {}y^{\prime } = \cot \left (x \right ) \cot \left (y\right ) \]

[_separable]

1.977

4717

\[ {}y^{\prime }+\cot \left (x \right ) \cot \left (y\right ) = 0 \]

[_separable]

2.075

4718

\[ {}y^{\prime } = \sin \left (x \right ) \left (\csc \left (y\right )-\cot \left (y\right )\right ) \]

[_separable]

3.218

4719

\[ {}y^{\prime } = \tan \left (x \right ) \cot \left (y\right ) \]

[_separable]

1.858

4720

\[ {}y^{\prime }+\tan \left (x \right ) \cot \left (y\right ) = 0 \]

[_separable]

1.852

4721

\[ {}y^{\prime }+\sin \left (2 x \right ) \csc \left (2 y\right ) = 0 \]

[_separable]

6.009

4722

\[ {}y^{\prime } = \tan \left (x \right ) \left (\tan \left (y\right )+\sec \left (x \right ) \sec \left (y\right )\right ) \]

[‘y=_G(x,y’)‘]

7.303

4723

\[ {}y^{\prime } = \cos \left (x \right ) \sec \left (y\right )^{2} \]

[_separable]

2.124

4724

\[ {}y^{\prime } = \sec \left (x \right )^{2} \sec \left (y\right )^{3} \]

[_separable]

2.095

4725

\[ {}y^{\prime } = a +b \sin \left (y\right ) \]

[_quadrature]

38.447

4726

\[ {}y^{\prime } = \left (1+\cos \left (x \right ) \sin \left (y\right )\right ) \tan \left (y\right ) \]

unknown

7.890

4727

\[ {}y^{\prime }+\csc \left (2 x \right ) \sin \left (2 y\right ) = 0 \]

[_separable]

5.028

4728

\[ {}y^{\prime }+f \left (x \right )+g \left (x \right ) \tan \left (y\right ) = 0 \]

[‘y=_G(x,y’)‘]

3.836

4729

\[ {}y^{\prime } = \sqrt {a +b \cos \left (y\right )} \]

[_quadrature]

11.815

4730

\[ {}y^{\prime } = {\mathrm e}^{y}+x \]

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

1.389

4731

\[ {}y^{\prime } = {\mathrm e}^{x +y} \]

[_separable]

2.665

4732

\[ {}y^{\prime } = {\mathrm e}^{x} \left (a +b \,{\mathrm e}^{-y}\right ) \]

[_separable]

1.875

4733

\[ {}y \ln \left (x \right ) \ln \left (y\right )+y^{\prime } = 0 \]

[_separable]

1.704

4734

\[ {}y^{\prime } = x^{m -1} y^{1-n} f \left (a \,x^{m}+b y^{n}\right ) \]

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

3.713

4735

\[ {}y^{\prime } = a f \left (y\right ) \]

[_quadrature]

1.068

4736

\[ {}y^{\prime } = f \left (a +b x +c y\right ) \]

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

1.138

4737

\[ {}y^{\prime } = f \left (x \right ) g \left (y\right ) \]

[_separable]

1.063

4738

\[ {}y^{\prime } = \sec \left (x \right )^{2}+y \sec \left (x \right ) \operatorname {Csx} \left (x \right ) \]

[_linear]

1.448

4739

\[ {}2 y^{\prime } = 2 \sin \left (y\right )^{2} \tan \left (y\right )-x \sin \left (2 y\right ) \]

[‘y=_G(x,y’)‘]

44.194

4740

\[ {}2 y^{\prime }+a x = \sqrt {a^{2} x^{2}-4 b \,x^{2}-4 c y} \]

[[_homogeneous, ‘class G‘]]

13.868

4741

\[ {}3 y^{\prime } = x +\sqrt {x^{2}-3 y} \]

[[_1st_order, _with_linear_symmetries], _dAlembert]

8.118

4742

\[ {}x y^{\prime } = \sqrt {a^{2}-x^{2}} \]

[_quadrature]

0.500

4743

\[ {}x y^{\prime }+x +y = 0 \]

[_linear]

2.765

4744

\[ {}x y^{\prime }+x^{2}-y = 0 \]

[_linear]

1.607

4745

\[ {}x y^{\prime } = x^{3}-y \]

[_linear]

1.504

4746

\[ {}x y^{\prime } = 1+x^{3}+y \]

[_linear]

1.365

4747

\[ {}x y^{\prime } = x^{m}+y \]

[_linear]

0.728

4748

\[ {}x y^{\prime } = x \sin \left (x \right )-y \]

[_linear]

1.415

4749

\[ {}x y^{\prime } = x^{2} \sin \left (x \right )+y \]

[_linear]

1.572

4750

\[ {}x y^{\prime } = x^{n} \ln \left (x \right )-y \]

[_linear]

1.246

4751

\[ {}x y^{\prime } = \sin \left (x \right )-2 y \]

[_linear]

1.493

4752

\[ {}x y^{\prime } = a y \]

[_separable]

1.204

4753

\[ {}x y^{\prime } = 1+x +a y \]

[_linear]

1.595

4754

\[ {}x y^{\prime } = a x +b y \]

[_linear]

2.328

4755

\[ {}x y^{\prime } = a \,x^{2}+b y \]

[_linear]

1.415

4756

\[ {}x y^{\prime } = a +b \,x^{n}+c y \]

[_linear]

1.297

4757

\[ {}x y^{\prime }+2+\left (3-x \right ) y = 0 \]

[_linear]

1.290

4758

\[ {}x y^{\prime }+x +\left (a x +2\right ) y = 0 \]

[_linear]

1.078

4759

\[ {}x y^{\prime }+\left (b x +a \right ) y = 0 \]

[_separable]

1.098

4760

\[ {}x y^{\prime } = x^{3}+\left (-2 x^{2}+1\right ) y \]

[_linear]

1.570

4761

\[ {}x y^{\prime } = a x -\left (-b \,x^{2}+1\right ) y \]

[_linear]

1.145

4762

\[ {}x y^{\prime }+x +\left (-a \,x^{2}+2\right ) y = 0 \]

[_linear]

1.188

4763

\[ {}x y^{\prime }+x^{2}+y^{2} = 0 \]

[_rational, _Riccati]

1.155

4764

\[ {}x y^{\prime } = x^{2}+y \left (y+1\right ) \]

[[_homogeneous, ‘class D‘], _rational, _Riccati]

1.683

4765

\[ {}x y^{\prime }-y+y^{2} = x^{{2}/{3}} \]

[_rational, _Riccati]

11.772

4766

\[ {}x y^{\prime } = a +b y^{2} \]

[_separable]

1.477

4767

\[ {}x y^{\prime } = a \,x^{2}+y+b y^{2} \]

[[_homogeneous, ‘class D‘], _rational, _Riccati]

1.372

4768

\[ {}x y^{\prime } = a \,x^{2 n}+\left (n +b y\right ) y \]

[_rational, _Riccati]

2.848

4769

\[ {}x y^{\prime } = a \,x^{n}+b y+c y^{2} \]

[_rational, _Riccati]

2.379

4770

\[ {}x y^{\prime } = k +a \,x^{n}+b y+c y^{2} \]

[_rational, _Riccati]

2.458

4771

\[ {}x y^{\prime }+a +x y^{2} = 0 \]

[_rational, [_Riccati, _special]]

1.087

4772

\[ {}x y^{\prime }+\left (1-x y\right ) y = 0 \]

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

1.630

4773

\[ {}x y^{\prime } = \left (1-x y\right ) y \]

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

2.498

4774

\[ {}x y^{\prime } = \left (1+x y\right ) y \]

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

2.480

4775

\[ {}x y^{\prime } = a \,x^{3} \left (1-x y\right ) y \]

[_Bernoulli]

1.319

4776

\[ {}x y^{\prime } = x^{3}+\left (2 x^{2}+1\right ) y+x y^{2} \]

[[_homogeneous, ‘class D‘], _rational, _Riccati]

1.975

4777

\[ {}x y^{\prime } = y \left (2 x y+1\right ) \]

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

2.384

4778

\[ {}x y^{\prime }+b x +\left (2+y a x \right ) y = 0 \]

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

2.169

4779

\[ {}x y^{\prime }+\operatorname {a0} +\operatorname {a1} x +\left (\operatorname {a2} +\operatorname {a3} x y\right ) y = 0 \]

[_rational, _Riccati]

6.668

4780

\[ {}x y^{\prime }+a \,x^{2} y^{2}+2 y = b \]

[_rational, _Riccati]

1.514

4781

\[ {}x y^{\prime }+x^{m}+\frac {\left (n -m \right ) y}{2}+x^{n} y^{2} = 0 \]

[_rational, _Riccati]

2.255

4782

\[ {}x y^{\prime }+\left (a +b \,x^{n} y\right ) y = 0 \]

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

1.760

4783

\[ {}x y^{\prime } = a \,x^{m}-b y-c \,x^{n} y^{2} \]

[_rational, _Riccati]

3.286

4784

\[ {}x y^{\prime } = 2 x -y+a \,x^{n} \left (x -y\right )^{2} \]

[[_1st_order, _with_linear_symmetries], _rational, _Riccati]

3.069

4785

\[ {}x y^{\prime }+\left (1-a y \ln \left (x \right )\right ) y = 0 \]

[_Bernoulli]

2.145

4786

\[ {}x y^{\prime } = y+\left (x^{2}-y^{2}\right ) f \left (x \right ) \]

[[_homogeneous, ‘class D‘], _Riccati]

2.020

4787

\[ {}x y^{\prime } = y \left (1+y^{2}\right ) \]

[_separable]

4.719

4788

\[ {}x y^{\prime }+y \left (1-x y^{2}\right ) = 0 \]

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

3.800

4789

\[ {}x y^{\prime }+y = a \left (x^{2}+1\right ) y^{3} \]

[_rational, _Bernoulli]

3.021

4790

\[ {}x y^{\prime } = a y+b \left (x^{2}+1\right ) y^{3} \]

[_rational, _Bernoulli]

3.674

4791

\[ {}x y^{\prime }+2 y = a \,x^{2 k} y^{k} \]

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

4.405

4792

\[ {}x y^{\prime } = 4 y-4 \sqrt {y} \]

[_separable]

3.608

4793

\[ {}x y^{\prime }+2 y = \sqrt {1+y^{2}} \]

[_separable]

3.556

4794

\[ {}x y^{\prime } = y+\sqrt {x^{2}+y^{2}} \]

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

8.355

4795

\[ {}x y^{\prime } = y+\sqrt {x^{2}-y^{2}} \]

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

97.385

4796

\[ {}x y^{\prime } = y+x \sqrt {x^{2}+y^{2}} \]

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

3.550

4797

\[ {}x y^{\prime } = y-x \left (x -y\right ) \sqrt {x^{2}+y^{2}} \]

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

5.274

4798

\[ {}x y^{\prime } = y+a \sqrt {y^{2}+b^{2} x^{2}} \]

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

11.652

4799

\[ {}x y^{\prime }+\left (\sin \left (y\right )-3 x^{2} \cos \left (y\right )\right ) \cos \left (y\right ) = 0 \]

[‘y=_G(x,y’)‘]

2.774

4800

\[ {}x y^{\prime }+x -y+x \cos \left (\frac {y}{x}\right ) = 0 \]

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

3.326