2.2.146 Problems 14501 to 14600

Table 2.305: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

Maple

Mma

Sympy

time(sec)

14501

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

[_linear]

2.863

14502

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

[_separable]

2.573

14503

\begin{align*} r^{\prime }+r \tan \left (t \right )&=\cos \left (t \right )^{2} \\ r \left (\frac {\pi }{4}\right ) &= 1 \\ \end{align*}

[_linear]

2.725

14504

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

[[_linear, ‘class A‘]]

2.137

14505

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

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

5.567

14506

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

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

8.032

14507

\begin{align*} y^{\prime }+y&=\left \{\begin {array}{cc} 2 & 0\le x <1 \\ 0 & 1\le x \end {array}\right . \\ y \left (0\right ) &= 0 \\ \end{align*}

[[_linear, ‘class A‘]]

1.589

14508

\begin{align*} y^{\prime }+y&=\left \{\begin {array}{cc} 5 & 0\le x <10 \\ 1 & 10\le x \end {array}\right . \\ y \left (0\right ) &= 6 \\ \end{align*}

[[_linear, ‘class A‘]]

2.725

14509

\begin{align*} y^{\prime }+y&=\left \{\begin {array}{cc} {\mathrm e}^{-x} & 0\le x <2 \\ {\mathrm e}^{-2} & 2\le x \end {array}\right . \\ y \left (0\right ) &= 1 \\ \end{align*}

[[_linear, ‘class A‘]]

1.744

14510

\begin{align*} \left (2+x \right ) y^{\prime }+y&=\left \{\begin {array}{cc} 2 x & 0\le x <2 \\ 4 & 2\le x \end {array}\right . \\ y \left (0\right ) &= 4 \\ \end{align*}

[_linear]

1.438

14511

\begin{align*} a y^{\prime }+b y&=k \,{\mathrm e}^{-\lambda x} \\ \end{align*}

[[_linear, ‘class A‘]]

2.652

14512

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

[[_linear, ‘class A‘]]

2.825

14513

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

[‘y=_G(x,y’)‘]

2.681

14514

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

[_separable]

4.141

14515

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

[_Riccati]

3.955

14516

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

[_Riccati]

2.333

14517

\begin{align*} y^{\prime }&=-8 x y^{2}+4 x \left (4 x +1\right ) y-8 x^{3}-4 x^{2}+1 \\ \end{align*}

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

5.911

14518

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

[_separable]

2.783

14519

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

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

4.462

14520

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

[_separable]

2.707

14521

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

[_linear]

2.225

14522

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

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

29.517

14523

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

[_separable]

0.222

14524

\begin{align*} 8 x^{3} y-12 x^{3}+\left (x^{4}+1\right ) y^{\prime }&=0 \\ \end{align*}

[_separable]

2.947

14525

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

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

14.710

14526

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

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

5.487

14527

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

[_linear]

3.329

14528

\begin{align*} y^{\prime }&=\frac {2 x -7 y}{3 y-8 x} \\ \end{align*}

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

29.941

14529

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

[_separable]

10.057

14530

\begin{align*} \left (x^{3}+1\right ) y^{\prime }+6 x^{2} y&=6 x^{2} \\ \end{align*}

[_separable]

2.985

14531

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

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

14.881

14532

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

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

10.211

14533

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

[_separable]

4.638

14534

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

[_exact, _Bernoulli]

4.210

14535

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

[_exact, _rational]

15.507

14536

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

[_separable]

5.511

14537

\begin{align*} y^{\prime }&=\frac {2 x +7 y}{2 x -2 y} \\ y \left (1\right ) &= 2 \\ \end{align*}

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

22.271

14538

\begin{align*} y^{\prime }&=\frac {x y}{x^{2}+1} \\ y \left (\sqrt {15}\right ) &= 2 \\ \end{align*}

[_separable]

4.175

14539

\begin{align*} y^{\prime }+y&=\left \{\begin {array}{cc} 1 & 0\le x <2 \\ 0 & 0<x \end {array}\right . \\ y \left (0\right ) &= 0 \\ \end{align*}

[[_linear, ‘class A‘]]

1.361

14540

\begin{align*} \left (2+x \right ) y^{\prime }+y&=\left \{\begin {array}{cc} 2 x & 0\le x \le 2 \\ 4 & 2<x \end {array}\right . \\ y \left (0\right ) &= 4 \\ \end{align*}

[_linear]

0.648

14541

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

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

77.592

14542

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

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

2.777

14543

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

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

3.131

14544

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

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

3.293

14545

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

[_rational]

3.667

14546

\begin{align*} 4 x y^{2}+6 y+\left (5 x^{2} y+8 x \right ) y^{\prime }&=0 \\ \end{align*}

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

6.434

14547

\begin{align*} 8 x^{2} y^{3}-2 y^{4}+\left (5 x^{3} y^{2}-8 x y^{3}\right ) y^{\prime }&=0 \\ \end{align*}

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

1.166

14548

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

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

5.063

14549

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

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

7.701

14550

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

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

16.497

14551

\begin{align*} 10 x -4 y+12-\left (x +5 y+3\right ) y^{\prime }&=0 \\ \end{align*}

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

28.815

14552

\begin{align*} 6 x +4 y+1+\left (4 x +2 y+2\right ) y^{\prime }&=0 \\ y \left (\frac {1}{2}\right ) &= 3 \\ \end{align*}

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

7.020

14553

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

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

43.209

14554

\begin{align*} 2 x +3 y+1+\left (4 x +6 y+1\right ) y^{\prime }&=0 \\ y \left (-2\right ) &= 2 \\ \end{align*}

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

8.243

14555

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

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

29.362

14556

\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&={\mathrm e}^{x} \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= 7 \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

2.558

14557

\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&={\mathrm e}^{x} \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (1\right ) &= 7 \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

1.425

14558

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

[[_2nd_order, _with_linear_symmetries]]

4.095

14559

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

[[_2nd_order, _missing_x]]

4.530

14560

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

[[_2nd_order, _missing_x]]

6.471

14561

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

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

5.316

14562

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

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

4.461

14563

\begin{align*} y^{\prime \prime }-5 y^{\prime }+4 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

4.549

14564

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+5 y^{\prime }+12 y&=0 \\ \end{align*}

[[_3rd_order, _missing_x]]

0.057

14565

\begin{align*} x^{3} y^{\prime \prime \prime }-4 x^{2} y^{\prime \prime }+8 y^{\prime } x -8 y&=0 \\ \end{align*}

[[_3rd_order, _with_linear_symmetries]]

0.151

14566

\begin{align*} x^{2} y^{\prime \prime }-4 y^{\prime } x +4 y&=0 \\ \end{align*}

[[_Emden, _Fowler]]

0.108

14567

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

[[_2nd_order, _with_linear_symmetries]]

0.122

14568

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

[_Gegenbauer]

0.115

14569

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

[[_2nd_order, _with_linear_symmetries]]

0.121

14570

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

[[_2nd_order, _with_linear_symmetries]]

0.123

14571

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

[[_2nd_order, _with_linear_symmetries]]

0.150

14572

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

[[_2nd_order, _with_linear_symmetries]]

29.234

14573

\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=2-12 x +6 \,{\mathrm e}^{x} \\ \end{align*}

[[_2nd_order, _with_linear_symmetries]]

30.164

14574

\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

4.293

14575

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

[[_2nd_order, _missing_x]]

4.707

14576

\begin{align*} 4 y^{\prime \prime }-12 y^{\prime }+5 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

5.000

14577

\begin{align*} 3 y^{\prime \prime }-14 y^{\prime }-5 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

5.077

14578

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

[[_3rd_order, _missing_x]]

0.057

14579

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+5 y^{\prime }+12 y&=0 \\ \end{align*}

[[_3rd_order, _missing_x]]

0.064

14580

\begin{align*} y^{\prime \prime }-8 y^{\prime }+16 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

5.362

14581

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

[[_2nd_order, _missing_x]]

6.860

14582

\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

6.393

14583

\begin{align*} y^{\prime \prime }+6 y^{\prime }+25 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

20.211

14584

\begin{align*} y^{\prime \prime }+9 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

4.358

14585

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

[[_2nd_order, _missing_x]]

2.810

14586

\begin{align*} y^{\prime \prime \prime }-5 y^{\prime \prime }+7 y^{\prime }-3 y&=0 \\ \end{align*}

[[_3rd_order, _missing_x]]

0.065

14587

\begin{align*} 4 y^{\prime \prime \prime }+4 y^{\prime \prime }-7 y^{\prime }+2 y&=0 \\ \end{align*}

[[_3rd_order, _missing_x]]

0.065

14588

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y&=0 \\ \end{align*}

[[_3rd_order, _missing_x]]

0.068

14589

\begin{align*} y^{\prime \prime \prime }+4 y^{\prime \prime }+5 y^{\prime }+6 y&=0 \\ \end{align*}

[[_3rd_order, _missing_x]]

0.071

14590

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

[[_3rd_order, _missing_x]]

0.066

14591

\begin{align*} y^{\prime \prime \prime \prime }+8 y^{\prime \prime }+16 y&=0 \\ \end{align*}

[[_high_order, _missing_x]]

0.078

14592

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

[[_high_order, _missing_x]]

0.070

14593

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

[[_high_order, _missing_x]]

0.070

14594

\begin{align*} y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }-2 y^{\prime \prime }+2 y^{\prime }+12 y&=0 \\ \end{align*}

[[_high_order, _missing_x]]

0.078

14595

\begin{align*} y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+15 y^{\prime \prime }+20 y^{\prime }+12 y&=0 \\ \end{align*}

[[_high_order, _missing_x]]

0.079

14596

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

[[_high_order, _missing_x]]

0.062

14597

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

[[_high_order, _quadrature]]

0.046

14598

\begin{align*} y^{\prime \prime }-y^{\prime }-12 y&=0 \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}

[[_2nd_order, _missing_x]]

0.791

14599

\begin{align*} y^{\prime \prime }+7 y^{\prime }+10 y&=0 \\ y \left (0\right ) &= -4 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}

[[_2nd_order, _missing_x]]

1.285

14600

\begin{align*} y^{\prime \prime }-6 y^{\prime }+8 y&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 6 \\ \end{align*}

[[_2nd_order, _missing_x]]

1.040