2.2.37 Problems 3601 to 3700

Table 2.87: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

Maple

Mma

Sympy

time(sec)

3601

\begin{align*} y^{\prime }&=\frac {x^{2} y-32}{-x^{2}+16}+2 \\ \end{align*}

[_separable]

3.822

3602

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

[_separable]

6.017

3603

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

[_separable]

4.389

3604

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

[_separable]

3.042

3605

\begin{align*} y^{\prime }&=1-\frac {\sin \left (x +y\right )}{\cos \left (x \right ) \sin \left (y\right )} \\ y \left (\frac {\pi }{4}\right ) &= \frac {\pi }{4} \\ \end{align*}

[_separable]

4.435

3606

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

[_separable]

5.044

3607

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

[_quadrature]

1.863

3608

\begin{align*} m v^{\prime }&=m g -k v^{2} \\ v \left (0\right ) &= 0 \\ \end{align*}

[_quadrature]

8.292

3609

\begin{align*} y^{\prime }+y&=4 \,{\mathrm e}^{x} \\ \end{align*}

[[_linear, ‘class A‘]]

0.154

3610

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

[_linear]

0.111

3611

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

[_linear]

0.105

3612

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

[_linear]

0.112

3613

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

[_linear]

0.119

3614

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

[_linear]

0.104

3615

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

[_linear]

0.167

3616

\begin{align*} y^{\prime }+\frac {y}{x \ln \left (x \right )}&=9 x^{2} \\ \end{align*}

[_linear]

0.168

3617

\begin{align*} y^{\prime }-\tan \left (x \right ) y&=8 \sin \left (x \right )^{3} \\ \end{align*}

[_linear]

0.115

3618

\begin{align*} t x^{\prime }+2 x&=4 \,{\mathrm e}^{t} \\ \end{align*}

[_linear]

0.139

3619

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

[_linear]

2.682

3620

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

[_linear]

0.134

3621

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

[_linear]

0.141

3622

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

[[_linear, ‘class A‘]]

0.153

3623

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

[_linear]

0.245

3624

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

[_linear]

0.228

3625

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

[_linear]

3.878

3626

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

[_linear]

4.600

3627

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

[[_linear, ‘class A‘]]

2.050

3628

\begin{align*} y^{\prime }-2 y&=\left \{\begin {array}{cc} 1 & x \le 1 \\ 0 & 1<x \end {array}\right . \\ y \left (0\right ) &= 3 \\ \end{align*}

[[_linear, ‘class A‘]]

1.611

3629

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

[[_linear, ‘class A‘]]

1.647

3630

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

[[_2nd_order, _missing_y]]

3.367

3631

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

[_linear]

2.169

3632

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

[[_linear, ‘class A‘]]

1.895

3633

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

[_linear]

2.466

3634

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

[_linear]

3.232

3635

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

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

6.075

3636

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

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

16.378

3637

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

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

5.671

3638

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

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

6.781

3639

\begin{align*} y^{\prime } x&=\sqrt {16 x^{2}-y^{2}}+y \\ \end{align*}

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

60.969

3640

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

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

23.306

3641

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

[_separable]

0.150

3642

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

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

19.984

3643

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

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

3.000

3644

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

[[_homogeneous, ‘class A‘]]

6.474

3645

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

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

5.773

3646

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

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

34.474

3647

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

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

19.424

3648

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

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

7.798

3649

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

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

50.497

3650

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

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

39.998

3651

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

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

19.953

3652

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

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

24.100

3653

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

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

61.646

3654

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

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

25.559

3655

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

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

27.024

3656

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

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

6.939

3657

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

[_Bernoulli]

11.518

3658

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

[_Bernoulli]

6.761

3659

\begin{align*} y^{\prime }+\frac {2 y}{x}&=6 \sqrt {x^{2}+1}\, \sqrt {y} \\ \end{align*}

[_Bernoulli]

5.177

3660

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

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

8.036

3661

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

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

19.030

3662

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

[_rational, _Bernoulli]

6.428

3663

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

[_Bernoulli]

8.715

3664

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

[_Bernoulli]

3.928

3665

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

[_Bernoulli]

5.427

3666

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

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

18.487

3667

\begin{align*} 2 y^{\prime }+\cot \left (x \right ) y&=\frac {8 \cos \left (x \right )^{3}}{y} \\ \end{align*}

[_Bernoulli]

83.427

3668

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

[_separable]

20.065

3669

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

[_rational, _Bernoulli]

3.212

3670

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

[_Bernoulli]

6.069

3671

\begin{align*} y^{\prime }&=\left (9 x -y\right )^{2} \\ y \left (0\right ) &= 0 \\ \end{align*}

[[_homogeneous, ‘class C‘], _Riccati]

3.852

3672

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

[[_homogeneous, ‘class C‘], _Riccati]

9.242

3673

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

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

6.220

3674

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

[[_homogeneous, ‘class G‘]]

7.117

3675

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

[[_1st_order, _with_linear_symmetries], _Riccati]

6.546

3676

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

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

36.567

3677

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

[_Riccati]

11.171

3678

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

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

16.874

3679

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

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

4.322

3680

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

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

3.658

3681

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

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

22.917

3682

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

[_separable]

86.557

3683

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

[‘x=_G(y,y’)‘]

3.791

3684

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

[[_homogeneous, ‘class G‘], _exact]

0.311

3685

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

[_linear]

0.195

3686

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

[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]

0.296

3687

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

[_separable]

0.121

3688

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

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

0.623

3689

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

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

0.188

3690

\begin{align*} \frac {1}{x}-\frac {y}{x^{2}+y^{2}}+\frac {x y^{\prime }}{x^{2}+y^{2}}&=0 \\ \end{align*}

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

0.324

3691

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

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

0.229

3692

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

[_exact, _Bernoulli]

0.744

3693

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

[_exact]

0.204

3694

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

[_exact]

0.300

3695

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

[[_2nd_order, _missing_x]]

5.566

3696

\begin{align*} y^{\prime \prime }+7 y^{\prime }+10 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

5.359

3697

\begin{align*} y^{\prime \prime }-36 y&=0 \\ \end{align*}

[[_2nd_order, _missing_x]]

4.676

3698

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

[[_2nd_order, _missing_x]]

2.586

3699

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

[[_3rd_order, _missing_x]]

0.073

3700

\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y^{\prime }-12 y&=0 \\ \end{align*}

[[_3rd_order, _missing_x]]

0.080