2.2.141 Problems 14001 to 14100

Table 2.299: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

Maple

Mma

Sympy

time(sec)

14001

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

[‘y=_G(x,y’)‘]

14.428

14002

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

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

18.590

14003

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

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

30.736

14004

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

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

7.553

14005

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

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

4.086

14006

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

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

36.036

14007

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

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

3.700

14008

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

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

5.262

14009

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

[_separable]

0.428

14010

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

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

60.839

14011

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

[_linear]

5.458

14012

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

[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]

8.019

14013

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

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

17.555

14014

\begin{align*} x y^{\prime }-a y+b y^{2}&=c \,x^{2 a} \\ \end{align*}

[_rational, _Riccati]

7.320

14015

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

[_separable]

9.548

14016

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

[_separable]

36.295

14017

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

[_linear]

5.277

14018

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

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

10.411

14019

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

[_Bernoulli]

8.623

14020

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

[_separable]

7.241

14021

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

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

22.279

14022

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

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

19.194

14023

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

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

53.450

14024

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

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

17.528

14025

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

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

3.969

14026

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

[_linear]

13.203

14027

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

[_separable]

13.158

14028

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

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

42.439

14029

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

[_linear]

5.521

14030

\begin{align*} 5 y x -3 y^{3}+\left (3 x^{2}-7 x y^{2}\right ) y^{\prime }&=0 \\ \end{align*}

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

13.957

14031

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

[_linear]

4.372

14032

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

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

12.417

14033

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

[_separable]

7.247

14034

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

[_separable]

10.939

14035

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

[_rational]

5.239

14036

\begin{align*} 2 x +3 y-1+\left (2 x +3 y-5\right ) y^{\prime }&=0 \\ \end{align*}

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

15.404

14037

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

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

42.540

14038

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

[_rational]

4.618

14039

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

[[_1st_order, _with_linear_symmetries]]

10.235

14040

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

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

19.237

14041

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

[_Bernoulli]

11.599

14042

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

[_rational]

3.338

14043

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

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

36.996

14044

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

[_quadrature]

1.001

14045

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

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

2.369

14046

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

[_quadrature]

2.227

14047

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

[_linear]

1.493

14048

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

[_quadrature]

1.346

14049

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

[_quadrature]

0.941

14050

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

[[_1st_order, _with_linear_symmetries], _dAlembert]

12.415

14051

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

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

4.273

14052

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

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

2.203

14053

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

[[_homogeneous, ‘class C‘], _Riccati]

4.775

14054

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

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

3.588

14055

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

[[_1st_order, _with_linear_symmetries], _dAlembert]

4.659

14056

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

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

6.531

14057

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

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

1.886

14058

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

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

2.201

14059

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

[[_1st_order, _with_linear_symmetries]]

1.127

14060

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

[[_1st_order, _with_linear_symmetries], _rational, _Clairaut]

1.007

14061

\begin{align*} 4 \,{\mathrm e}^{2 y} {y^{\prime }}^{2}+2 x y^{\prime }-1&=0 \\ \end{align*}

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

1.159

14062

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

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

4.445

14063

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

[‘y=_G(x,y’)‘]

31.868

14064

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

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

7.089

14065

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

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

106.999

14066

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

[[_1st_order, _with_linear_symmetries]]

1.177

14067

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

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

1.664

14068

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

[‘y=_G(x,y’)‘]

66.469

14069

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

[_quadrature]

1.449

14070

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

[[_1st_order, _with_linear_symmetries], _Clairaut]

0.851

14071

\begin{align*} x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+1&=0 \\ \end{align*}

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

4.730

14072

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

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

3.851

14073

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

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

4.440

14074

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

[_rational]

135.917

14075

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

[_separable]

3.446

14076

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

[[_1st_order, _with_linear_symmetries], _rational, _Clairaut]

1.039

14077

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

[_separable]

0.594

14078

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

[[_1st_order, _with_linear_symmetries]]

4.264

14079

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

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

21.478

14080

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

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

4.367

14081

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

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

2.292

14082

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

[[_homogeneous, ‘class G‘], _Clairaut]

4.073

14083

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

[_quadrature]

0.662

14084

\begin{align*} 8 \left (y^{\prime }+1\right )^{3}&=27 \left (x +y\right ) \left (1-y^{\prime }\right )^{3} \\ \end{align*}

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

22.626

14085

\begin{align*} 4 {y^{\prime }}^{2}&=9 x \\ \end{align*}

[_quadrature]

2.034

14086

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

[_quadrature]

2.133

14087

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

[[_2nd_order, _missing_x]]

0.421

14088

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

[[_2nd_order, _missing_x]]

0.572

14089

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

[[_3rd_order, _missing_x]]

0.090

14090

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

[[_3rd_order, _missing_x]]

0.096

14091

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

[[_3rd_order, _missing_x]]

0.111

14092

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

[[_3rd_order, _missing_x]]

0.100

14093

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

[[_high_order, _missing_x]]

0.117

14094

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+9 y^{\prime }&=0 \\ \end{align*}

[[_3rd_order, _missing_x]]

0.098

14095

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

[[_high_order, _missing_x]]

0.121

14096

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

[[_3rd_order, _missing_x]]

0.101

14097

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

[[_3rd_order, _missing_y]]

0.233

14098

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.775

14099

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

[[_3rd_order, _linear, _nonhomogeneous]]

0.294

14100

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

[[_2nd_order, _linear, _nonhomogeneous]]

0.920