2.2.47 Problems 4601 to 4700

Table 2.95: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

4601

x2y+(12x+x2)y+xy=0

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

0.650

4602

x2y+(x2+x)y(x+1)y=0

[[_2nd_order, _with_linear_symmetries]]

0.731

4603

x2y+2xy(x2+2)y=0

[[_2nd_order, _with_linear_symmetries]]

0.662

4604

xy2xyy=0

[[_2nd_order, _with_linear_symmetries]]

1.283

4605

xy+2yxy=0

[[_2nd_order, _with_linear_symmetries]]

0.582

4606

x2yx2y+2(1+x)y=0

[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]]

1.371

4607

xy+yxy=0

[[_2nd_order, _with_linear_symmetries]]

0.418

4608

y=af(x)

[_quadrature]

0.179

4609

y=x+sin(x)+y

[[_linear, ‘class A‘]]

1.727

4610

y=x2+3cosh(x)+2y

[[_linear, ‘class A‘]]

1.942

4611

y=a+bx+cy

[[_linear, ‘class A‘]]

0.836

4612

y=acos(bx+c)+ky

[[_linear, ‘class A‘]]

1.622

4613

y=asin(bx+c)+ky

[[_linear, ‘class A‘]]

1.629

4614

y=a+bekx+cy

[[_linear, ‘class A‘]]

1.085

4615

y=x(x2y)

[_linear]

1.572

4616

y=x(ex2+ay)

[_linear]

1.364

4617

y=x2(ax3+by)

[_linear]

2.057

4618

y=axny

[_separable]

1.275

4619

y=sin(x)cos(x)+ycos(x)

[_linear]

2.049

4620

y=esin(x)+ycos(x)

[_linear]

1.902

4621

y=ycot(x)

[_separable]

1.804

4622

y=1ycot(x)

[_linear]

1.427

4623

y=xcsc(x)ycot(x)

[_linear]

1.869

4624

y=(2csc(2x)+cot(x))y

[_separable]

3.955

4625

y=sec(x)ycot(x)

[_linear]

1.891

4626

y=exsin(x)+ycot(x)

[_linear]

2.374

4627

y+csc(x)+2ycot(x)=0

[_linear]

1.846

4628

y=4csc(x)xsec(x)22ycot(2x)

[_linear]

293.542

4629

y=2cot(x)2cos(2x)2ycsc(2x)

[_linear]

3.626

4630

y=4csc(x)x(sin(x)3+y)

[_linear]

12.154

4631

y=4csc(x)x(1tan(x)2+y)

[_linear]

89.384

4632

y=ysec(x)

[_separable]

2.090

4633

y+tan(x)=(1y)sec(x)

[_linear]

2.173

4634

y=ytan(x)

[_separable]

1.855

4635

y=cos(x)+ytan(x)

[_linear]

1.958

4636

y=cos(x)ytan(x)

[_linear]

1.862

4637

y=sec(x)ytan(x)

[_linear]

1.799

4638

y=sin(2x)+ytan(x)

[_linear]

2.039

4639

y=sin(2x)ytan(x)

[_linear]

2.006

4640

y=sin(x)+2ytan(x)

[_linear]

1.976

4641

y=2+2sec(2x)+2ytan(2x)

[_linear]

9.392

4642

y=csc(x)+3ytan(x)

[_linear]

2.047

4643

y=(a+cos(ln(x))+sin(ln(x)))y

[_separable]

1.992

4644

y=6e2xytanh(x)

[_linear]

2.041

4645

y=f(x)f(x)+f(x)y

[_linear]

0.582

4646

y=f(x)+g(x)y

[_linear]

1.055

4647

y=x2y2

[_Riccati]

1.182

4648

y+f(x)2=f(x)+y2

[_Riccati]

0.999

4649

y+1x=y(x+y)

[_Riccati]

1.545

4650

y=(x+y)2

[[_homogeneous, ‘class C‘], _Riccati]

1.629

4651

y=(xy)2

[[_homogeneous, ‘class C‘], _Riccati]

1.783

4652

y=33x+3y+(xy)2

[[_homogeneous, ‘class C‘], _Riccati]

3.256

4653

y=2x(x2+1)y+y2

[_Riccati]

1.706

4654

y=x(x3+2)(2x2y)y

[[_1st_order, _with_linear_symmetries], _Riccati]

1.195

4655

y=1+x(x3+2)+(2x2y)y

[[_1st_order, _with_linear_symmetries], _Riccati]

1.812

4656

y=cos(x)(sin(x)y)y

[_Riccati]

3.012

4657

y=cos(2x)+(sin(2x)+y)y

[_Riccati]

6.133

4658

y=f(x)+xf(x)y+y2

[_Riccati]

1.792

4659

y=(3+x4y)2

[[_homogeneous, ‘class C‘], _Riccati]

4.544

4660

y=(1+4x+9y)2

[[_homogeneous, ‘class C‘], _Riccati]

35.928

4661

y=3a+3bx+3by2

[_Riccati]

1.456

4662

y=a+by2

[_quadrature]

3.757

4663

y=ax+by2

[[_Riccati, _special]]

1.133

4664

y=a+bx+cy2

[_Riccati]

1.352

4665

y=axn1+bx2n+cy2

[_Riccati]

3.642

4666

y=ax2+by2

[[_Riccati, _special]]

1.321

4667

y=a0+a1y+a2y2

[_quadrature]

3.605

4668

y=f(x)+ay+by2

[_Riccati]

1.418

4669

y=1+a(xy)y

[_Riccati]

1.454

4670

y=f(x)+g(x)y+ay2

[_Riccati]

1.806

4671

y=xy(3+y)

[_separable]

2.872

4672

y=1xx3+(2x2+1)yxy2

[_Riccati]

2.817

4673

y=x(2+x2yy2)

[_Riccati]

1.793

4674

y=x+(12x)y(1x)y2

[_Riccati]

2.583

4675

y=axy2

[_separable]

1.385

4676

y=xn(a+by2)

[_separable]

3.237

4677

y=axm+bxny2

[_Riccati]

2.246

4678

y=(a+bycos(kx))y

[_Bernoulli]

2.249

4679

y=sin(x)(2sec(x)2y)

[_linear]

2.626

4680

y+4csc(x)=(3cot(x))y+y2sin(x)

[_Riccati]

6.687

4681

y=ysec(x)+(sin(x)1)2

[_linear]

3.356

4682

y+tan(x)(1y2)=0

[_separable]

2.717

4683

y=f(x)+g(x)y+h(x)y2

[_Riccati]

2.540

4684

y=(a+by+cy2)f(x)

[_separable]

3.531

4685

y+(ax+y)y2=0

[_Abel]

0.827

4686

y=(aex+y)y2

[_Abel]

1.369

4687

y+3a(y+2x)y2=0

[_Abel]

0.860

4688

y=y(a+by2)

[_quadrature]

8.071

4689

y=a0+a1y+a2y2+a3y3

[_quadrature]

73.996

4690

y=xy3

[_separable]

3.589

4691

y+y(1xy2)=0

[_Bernoulli]

2.944

4692

y=(a+bxy)y2

[[_homogeneous, ‘class G‘], _Abel]

2.389

4693

y+2xy(1+axy2)=0

[_Bernoulli]

1.350

4694

y+(tan(x)+y2sec(x))y=0

[_Bernoulli]

3.049

4695

y+y3sec(x)tan(x)=0

[_separable]

3.568

4696

y=f0(x)+f1(x)y+f2(x)y2+f3(x)y3

[_Abel]

4.827

4697

y=axn1n+byn

[[_homogeneous, ‘class G‘], _Chini]

2.235

4698

y=f(x)y+g(x)yk

[_Bernoulli]

1.768

4699

y=f(x)+g(x)y+h(x)yn

[_Chini]

3.246

4700

y=|y|

[_quadrature]

2.860