2.2.141 Problems 14001 to 14100

Table 2.295: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

Maple

Mma

Sympy

time(sec)

14001

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

[‘y=_G(x,y’)‘]

6.043

14002

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

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

6.947

14003

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

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

20.465

14004

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

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

3.903

14005

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

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

2.433

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‘]]

21.022

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]‘]]

2.418

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]‘]]

3.982

14009

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

[_separable]

0.152

14010

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

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

87.367

14011

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

[_linear]

3.493

14012

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

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

3.360

14013

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

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

6.539

14014

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

[_rational, _Riccati]

5.533

14015

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

[_separable]

6.658

14016

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

[_separable]

17.108

14017

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

[_linear]

3.719

14018

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

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

5.019

14019

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

[_Bernoulli]

6.863

14020

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

[_separable]

4.548

14021

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

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

18.077

14022

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

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

32.586

14023

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

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

80.471

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]

7.069

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‘]]

0.952

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]

3.931

14027

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

[_separable]

2.870

14028

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

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

6.930

14029

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

[_linear]

2.126

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]

2.650

14031

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

[_linear]

2.480

14032

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

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

2.164

14033

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

[_separable]

1.882

14034

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

[_separable]

2.013

14035

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

[_rational]

3.914

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‘]]

4.391

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]

9.199

14038

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

[_rational]

1.845

14039

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

[[_1st_order, _with_linear_symmetries]]

3.979

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]

4.964

14041

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

[_Bernoulli]

2.714

14042

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

[_rational]

2.720

14043

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

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

5.343

14044

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

[_quadrature]

0.126

14045

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

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

0.468

14046

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

[_quadrature]

0.355

14047

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

[_linear]

0.299

14048

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

[_quadrature]

0.231

14049

\begin{align*} {y^{\prime }}^{3}-\left (2 x +y^{2}\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]

0.184

14050

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

[[_1st_order, _with_linear_symmetries], _dAlembert]

2.766

14051

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

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

0.496

14052

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

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

0.431

14053

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

[[_homogeneous, ‘class C‘], _Riccati]

1.094

14054

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

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

0.364

14055

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

[[_1st_order, _with_linear_symmetries], _dAlembert]

0.296

14056

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

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

1.853

14057

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

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

0.391

14058

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

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

0.423

14059

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

[[_1st_order, _with_linear_symmetries]]

0.341

14060

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

[[_1st_order, _with_linear_symmetries], _rational, _Clairaut]

0.202

14061

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

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

0.270

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]

0.662

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’)‘]

24.651

14064

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

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

0.840

14065

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

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

53.471

14066

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

[[_1st_order, _with_linear_symmetries]]

0.385

14067

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

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

0.404

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’)‘]

56.862

14069

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

[_quadrature]

0.469

14070

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

[[_1st_order, _with_linear_symmetries], _Clairaut]

0.234

14071

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

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

0.507

14072

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

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

0.645

14073

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

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

0.701

14074

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

[_rational]

144.895

14075

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

[_separable]

0.914

14076

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

[[_1st_order, _with_linear_symmetries], _rational, _Clairaut]

0.240

14077

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

[_separable]

0.144

14078

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

[[_1st_order, _with_linear_symmetries]]

0.534

14079

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

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

6.428

14080

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

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

0.361

14081

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

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

0.434

14082

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

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

0.511

14083

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

[_quadrature]

0.131

14084

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

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

30.762

14085

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

[_quadrature]

0.304

14086

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

[_quadrature]

0.445

14087

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

[[_2nd_order, _missing_x]]

4.473

14088

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

[[_2nd_order, _missing_x]]

5.869

14089

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

[[_3rd_order, _missing_x]]

0.033

14090

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

[[_3rd_order, _missing_x]]

0.045

14091

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

[[_3rd_order, _missing_x]]

0.041

14092

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

[[_3rd_order, _missing_x]]

0.041

14093

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

[[_high_order, _missing_x]]

0.049

14094

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

[[_3rd_order, _missing_x]]

0.042

14095

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

[[_high_order, _missing_x]]

0.053

14096

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

[[_3rd_order, _missing_x]]

0.045

14097

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

[[_3rd_order, _missing_y]]

0.098

14098

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

[[_2nd_order, _linear, _nonhomogeneous]]

28.976

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]]

0.145

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]]

39.100