2.2.114 Problems 11301 to 11400

Table 2.229: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

time (sec)

11301

x2(x+1)y+2x(3x+2)y=0

[[_2nd_order, _missing_y]]

0.666

11302

y=2(x2)yx(x1)+2(x+1)yx2(x1)

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

0.764

11303

y=(5x4)yx(x1)(9x6)yx2(x1)

[[_2nd_order, _with_linear_symmetries]]

0.725

11304

y=((a+b+1)x+α+β1)yx(x1)(abxαβ)yx2(x1)

[[_2nd_order, _with_linear_symmetries]]

2.157

11305

y=yx+1yx(x+1)2

[[_2nd_order, _with_linear_symmetries]]

0.469

11306

y=2yx(x2)yx2(x2)

[[_2nd_order, _with_linear_symmetries]]

156.176

11307

y=2yx(x1)2

[[_2nd_order, _with_linear_symmetries]]

0.490

11308

y=((α+β+1)x2(α+β+1+a(γ+δ)δ)x+aγ)yx(x1)(xa)(αβxq)yx(x1)(xa)

[[_2nd_order, _with_linear_symmetries]]

3.413

11309

y=(Ax2+Bx+C)y(xa)(xb)(xc)(DDx+E)y(xa)(xb)(xc)

[[_2nd_order, _with_linear_symmetries]]

3.989

11310

y=(x4)y2x(x2)(x3)y2x2(x2)

[[_2nd_order, _with_linear_symmetries]]

0.685

11311

y=yx+1(3x+1)y4x2(x+1)

[[_2nd_order, _with_linear_symmetries]]

0.694

11312

y=(3x1)y2x(x1)+v(v+1)y4x2

[[_2nd_order, _with_linear_symmetries]]

1.513

11313

y=((a+1)x1)yx(x1)((a2b2)x+c2)y4x2(x1)

[[_2nd_order, _with_linear_symmetries]]

1.802

11314

y=(3x1)y2x(x1)(ax+b)y4x(x1)2

[[_2nd_order, _with_linear_symmetries]]

1.359

11315

y=(13x)y(x1)(2x1)2

[[_2nd_order, _with_linear_symmetries]]

0.578

11316

y=(3x+a+2b)y2(x+a)(x+b)(ab)y4(x+a)2(x+b)

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

3.413

11317

y=(6x1)y3x(x2)+y3x2(x2)

[[_2nd_order, _with_linear_symmetries]]

0.729

11318

y=(a(b+2)x2+(cd+1)x)y(ax+1)x2(abxcd)y(ax+1)x2

[[_2nd_order, _with_linear_symmetries]]

2.129

11319

y=2(ax+2b)yx(ax+b)(2ax+6b)y(ax+b)x2

[[_2nd_order, _with_linear_symmetries]]

0.795

11320

y=(2ax+b)yx(ax+b)(avxb)y(ax+b)x2+Ax

[[_2nd_order, _linear, _nonhomogeneous]]

147.196

11321

y=ayx4

[[_Emden, _Fowler]]

0.600

11322

y=(x2a(1a)b(x+b))yx4

[[_2nd_order, _with_linear_symmetries]]

0.966

11323

y=(e2xv2)yx4

[[_2nd_order, _with_linear_symmetries]]

0.581

11324

y=yx3+2yx4

[[_2nd_order, _with_linear_symmetries]]

0.510

11325

y=(a+b)yx2((a+b)x+ab)yx4

[[_2nd_order, _with_linear_symmetries]]

0.736

11326

y=yxyx4

[[_Emden, _Fowler]]

0.477

11327

y=yx(bx2+a(x4+1))yx4

[[_2nd_order, _with_linear_symmetries]]

1.171

11328

y=(x2+1)yx3yx4

[[_2nd_order, _with_linear_symmetries]]

1.132

11329

y=2yxa2yx4

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

0.853

11330

y=(2x2+1)yx3+yx4

[[_2nd_order, _with_linear_symmetries]]

0.548

11331

y=2(x+a)yx2byx4

[[_2nd_order, _with_linear_symmetries]]

1.005

11332

y=(2x21)yx3yx4

[[_2nd_order, _with_linear_symmetries]]

1.210

11333

y=(2x21)yx32yx4

[[_2nd_order, _with_linear_symmetries]]

0.903

11334

y=(x31)yx(x3+1)+xyx3+1

[[_2nd_order, _with_linear_symmetries]]

1.420

11335

y=(2x2+1)yx(x2+1)(v(v+1)x2n2)yx2(x2+1)

[[_2nd_order, _with_linear_symmetries]]

1.707

11336

y=(ax2+a1)yx(x2+1)(bx2+c)yx2(x2+1)

[[_2nd_order, _with_linear_symmetries]]

1.848

11337

y=(x22)yx(x21)(x22)yx2(x21)

[[_2nd_order, _with_linear_symmetries]]

0.825

11338

y=2xyx21v(v+1)yx2(x21)

[[_2nd_order, _with_linear_symmetries]]

1.574

11339

y=2xyx21+v(v+1)yx2

[[_2nd_order, _with_linear_symmetries]]

1.686

11340

y=2xyx21(a(a+1)ax2(a+3))yx2(x21)

[[_2nd_order, _with_linear_symmetries]]

1.127

11341

x2(x21)y2x3y((an)(a+n+1)x2(x21)+2ax2+n(n+1)(x21))y=0

[[_2nd_order, _with_linear_symmetries]]

2.958

11342

y=(ax2+a2)yx(x21)byx2

[[_2nd_order, _with_linear_symmetries]]

2.216

11343

y=(2bcxc(x21)+2(a1)x22a)yx(x21)(b2c2x2c(x21)+bcxc+2(2ac1)bcxc(2ac+1)+x2(a(a1)v(v+1))a(a+1))yx2(x21)

[[_2nd_order, _with_linear_symmetries]]

3.740

11344

y=ay(x2+1)2

[_Halm]

0.681

11345

y=2xyx2+1y(x2+1)2

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

0.700

11346

y=2xyx2+1(a2(x2+1)2n(n+1)(x2+1)+m2)y(x2+1)2

[[_2nd_order, _with_linear_symmetries]]

1.480

11347

y=axyx2+1by(x2+1)2

[[_2nd_order, _with_linear_symmetries]]

1.617

11348

y=ay(x21)2

[[_2nd_order, _with_linear_symmetries]]

0.684

11349

y=2xyx21+a2y(x21)2

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

0.925

11350

y=2xyx21(a2λ(x21))y(x21)2

[[_2nd_order, _with_linear_symmetries]]

1.535

11351

y=2xyx21((x21)(ax2+bx+c)k2)y(x21)2

[[_2nd_order, _with_linear_symmetries]]

1.815

11352

y=2xyx21(a2(x21)2n(n+1)(x21)m2)y(x21)2

[[_2nd_order, _with_linear_symmetries]]

1.679

11353

y=2x(2a1)yx21(x2(2a(2a1)v(v+1))+2a+v(v+1))y(x21)2

[[_2nd_order, _with_linear_symmetries]]

1.880

11354

y=2x(n+12a)yx21(4ax2(an)(x21)(2a+(vn)(v+n+1)))y(x21)2

[[_2nd_order, _with_linear_symmetries]]

2.052

11355

y=(2x2+a)yx(x2+a)byx2(x2+a)

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

2.172

11356

y=b2y(a2+x2)2

[[_Emden, _Fowler]]

0.897

11357

y=2(x21)yx(x1)2(2x2+2x+2)yx2(x1)2

[[_2nd_order, _with_linear_symmetries]]

0.589

11358

y=12y(x+1)2(x2+2x+3)

[[_2nd_order, _with_linear_symmetries]]

1.069

11359

y=byx2(xa)2

[[_2nd_order, _with_linear_symmetries]]

0.768

11360

y=byx2(xa)2+c

[[_2nd_order, _linear, _nonhomogeneous]]

1.835

11361

y=cy(xa)2(xb)2

[[_2nd_order, _with_linear_symmetries]]

1.073

11362

y=((α+β+1)(xa)2(xb)+(1αβ)(xb)2(xa))y(xa)2(xb)2αβ(ab)2y(xa)2(xb)2

[[_2nd_order, _with_linear_symmetries]]

1.647

11363

y=(x2(a21)+2(a+3)bxb2)y4x2

[[_2nd_order, _with_linear_symmetries]]

1.369

11364

y=(ax2+a3)y4(x2+1)2

[_Halm]

0.861

11365

y=18y(2x+1)2(x2+x+1)

[[_2nd_order, _with_linear_symmetries]]

1.060

11366

y=3y4(x2+x+1)2

[[_Emden, _Fowler]]

0.841

11367

y=(3x1)y2x(x1)(v(v+1)(x1)a2x)y4x2(x1)2

[[_2nd_order, _with_linear_symmetries]]

1.502

11368

y=(3x1)y2x(x1)(v(v+1)(x1)24n2x)y4x2(x1)2

[[_2nd_order, _with_linear_symmetries]]

1.614

11369

y=3y16x2(x1)2

[[_2nd_order, _with_linear_symmetries]]

0.550

11370

y=(7ax2+5)yx(ax2+1)(15ax2+5)yx2(ax2+1)

[[_2nd_order, _with_linear_symmetries]]

0.880

11371

y=bxy(x21)a(cx2+dx+e)ya(x21)2

[[_2nd_order, _with_linear_symmetries]]

1.920

11372

y=(bx2+cx+d)yax2(x1)2

[[_2nd_order, _with_linear_symmetries]]

1.309

11373

y=2yxcyx2(ax+b)2

[[_2nd_order, _with_linear_symmetries]]

0.884

11374

y=y(ax+b)4

[[_Emden, _Fowler]]

0.614

11375

y=Ay(ax2+bx+c)2

[[_Emden, _Fowler]]

1.150

11376

y=yx4+yx5

[[_2nd_order, _with_linear_symmetries]]

0.906

11377

y=(3x21)y(x21)x(x21(2v+1)2)y(x21)2

[[_2nd_order, _with_linear_symmetries]]

1.655

11378

y=(3x+1)y(x1)(x+1)36(x+1)2y(x1)2(3x+5)2

[[_2nd_order, _with_linear_symmetries]]

0.720

11379

y=yxayx6

[[_Emden, _Fowler]]

0.494

11380

y=(3x2+a)yx3byx6

[[_2nd_order, _with_linear_symmetries]]

0.974

11381

y=((14a)x21)yx(x21)((v2+x2)(x21)2+4a(a+1)x42ax2(x21))yx2(x21)2

[[_2nd_order, _with_linear_symmetries]]

4.779

11382

y=(1a1b1xc1+1a2b2xc2+1a3b3xc3)y(a1b1(c1c3)(c1c2)xc1+a2b2(c2c1)(c2c3)xc2+a3b3(c3c2)(c3c1)xc3)y(xc1)(xc2)(xc3)

[[_2nd_order, _with_linear_symmetries]]

10.230

11383

y=(2x2+1)yx3(2x2+1)y4x6

[[_2nd_order, _with_linear_symmetries]]

0.546

11384

y=(2x2+1)yx3(ax4+10x2+1)y4x6

[[_2nd_order, _with_linear_symmetries]]

0.683

11385

y=27xy16(x31)2

[[_2nd_order, _with_linear_symmetries]]

1.047

11386

y=((1al1bl1)b1b1xa1+(1al2bl2)b2b2xa2+(1al3bl3)b3b3xa3)y(al1bl1(a1b2a2b1)(a1b3+a3b1)b1xa1+al2bl2(a2b3a3b2)(a1b2a2b1)b2xa2+al3bl3(a1b3+a3b1)(a2b3a3b2)b3xa3)y(b1xa1)(b2xa2)(b3xa3)

[[_2nd_order, _with_linear_symmetries]]

12.697

11387

y=(x2((x2a1)(x2a2)+(x2a2)(x2a3)+(x2a3)(x2a1))(x2a1)(x2a2)(x2a3))yx(x2a1)(x2a2)(x2a3)(Ax2+B)yx(x2a1)(x2a2)(x2a3)

[[_2nd_order, _with_linear_symmetries]]

8.446

11388

y=ax2a1x2ayb2x2ay

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

0.651

11389

y=(apxb+q)yx(axb1)(arxb+s)yx2(axb1)

[[_2nd_order, _with_linear_symmetries]]

2.408

11390

y=yex+1

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

0.488

11391

y=yxln(x)+ln(x)2y

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

0.549

11392

y=yx(ln(x)1)yx2(ln(x)1)

[[_2nd_order, _with_linear_symmetries]]

0.543

11393

y=(a2sinh(x)2n(n1))ysinh(x)2

[[_2nd_order, _with_linear_symmetries]]

1.780

11394

y=2ncosh(x)ysinh(x)(a2+n2)y

[[_2nd_order, _with_linear_symmetries]]

2.342

11395

y=(2n+1)cos(x)ysin(x)(v+n+1)(vn)y

[[_2nd_order, _with_linear_symmetries]]

3.142

11396

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

[[_2nd_order, _with_linear_symmetries]]

1.505

11397

y=xsin(x)yxcos(x)sin(x)+sin(x)yxcos(x)sin(x)

[[_2nd_order, _with_linear_symmetries]]

2.199

11398

y=(x2sin(x)2xcos(x))yx2cos(x)(2cos(x)xsin(x))yx2cos(x)

[[_2nd_order, _with_linear_symmetries]]

1.079

11399

cos(x)2y(acos(x)2+n(n1))y=0

[[_2nd_order, _with_linear_symmetries]]

1.821

11400

y=a(n1)sin(2ax)ycos(ax)2na2((n1)sin(ax)2+cos(ax)2)ycos(ax)2

[[_2nd_order, _with_linear_symmetries]]

2.523