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’)‘]

4.894

14002

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

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

6.197

14003

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

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

23.608

14004

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

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

3.342

14005

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

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

2.050

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‘]]

10.760

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]‘]]

2.046

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]‘]]

3.674

14009

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

[_separable]

0.126

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]

39.985

14011

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

[_linear]

3.011

14012

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

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

3.100

14013

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

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

5.757

14014

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

[_rational, _Riccati]

4.734

14015

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

[_separable]

5.466

14016

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

[_separable]

7.421

14017

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

[_linear]

3.362

14018

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

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

4.942

14019

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

[_Bernoulli]

5.638

14020

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

[_separable]

4.303

14021

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

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

8.586

14022

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

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

11.640

14023

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

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

38.407

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]

6.376

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‘]]

0.989

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]

3.869

14027

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

[_separable]

2.890

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]

6.145

14029

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

[_linear]

1.954

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]

2.443

14031

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

[_linear]

2.670

14032

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

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

2.349

14033

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

[_separable]

2.045

14034

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

[_separable]

2.405

14035

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

[_rational]

4.853

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‘]]

5.236

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]

11.016

14038

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

[_rational]

2.148

14039

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

[[_1st_order, _with_linear_symmetries]]

4.551

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]

5.590

14041

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

[_Bernoulli]

3.167

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]

3.075

14043

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

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

6.059

14044

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

[_quadrature]

0.155

14045

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

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

0.549

14046

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

[_quadrature]

0.408

14047

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

[_linear]

0.365

14048

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

[_quadrature]

0.268

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]

0.240

14050

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

[[_1st_order, _with_linear_symmetries], _dAlembert]

3.132

14051

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

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

0.585

14052

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

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

0.513

14053

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

[[_homogeneous, ‘class C‘], _Riccati]

1.283

14054

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

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

0.434

14055

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

[[_1st_order, _with_linear_symmetries], _dAlembert]

0.364

14056

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

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

4.520

14057

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

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

0.456

14058

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

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

0.510

14059

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

[[_1st_order, _with_linear_symmetries]]

0.397

14060

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

[[_1st_order, _with_linear_symmetries], _rational, _Clairaut]

0.252

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)]‘]]

0.313

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]

0.773

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’)‘]

24.378

14064

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

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

0.957

14065

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

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

54.400

14066

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

[[_1st_order, _with_linear_symmetries]]

0.389

14067

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

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

0.390

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’)‘]

56.909

14069

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

[_quadrature]

0.467

14070

\begin{align*} y^{\prime } y&=\left (-b +x \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]

0.515

14072

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

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

0.650

14073

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

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

0.705

14074

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

[_rational]

145.536

14075

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

[_separable]

0.733

14076

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

[[_1st_order, _with_linear_symmetries], _rational, _Clairaut]

0.212

14077

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

[_separable]

0.127

14078

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

[[_1st_order, _with_linear_symmetries]]

0.498

14079

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

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

15.140

14080

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

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

0.377

14081

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

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

0.438

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]

0.417

14083

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

[_quadrature]

0.140

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]

32.235

14085

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

[_quadrature]

0.326

14086

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

[_quadrature]

0.449

14087

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

[[_2nd_order, _missing_x]]

0.178

14088

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

[[_2nd_order, _missing_x]]

0.234

14089

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

[[_3rd_order, _missing_x]]

0.065

14090

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

[[_3rd_order, _missing_x]]

0.040

14091

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

[[_3rd_order, _missing_x]]

0.040

14092

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

[[_3rd_order, _missing_x]]

0.040

14093

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

[[_high_order, _missing_x]]

0.043

14094

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

[[_3rd_order, _missing_x]]

0.040

14095

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

[[_high_order, _missing_x]]

0.051

14096

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

[[_3rd_order, _missing_x]]

0.042

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]]

1.382

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]]

0.137

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]]

1.388