2.16.112 Problems 11101 to 11200

Table 2.240: Main lookup table. Sorted sequentially by problem number.

#

ODE

Program classification

CAS classification

Solved?

Verified?

time (sec)

11101

\[ {}y^{\prime \prime }+\left (a +b \right ) {\mathrm e}^{\lambda x} y^{\prime }+a \,{\mathrm e}^{\lambda x} \left (b \,{\mathrm e}^{\lambda x}+\lambda \right ) y = 0 \]

unknown

[[_2nd_order, _with_linear_symmetries]]

N/A

0.825

11102

\[ {}y^{\prime \prime }+a \,{\mathrm e}^{\lambda x} y^{\prime }-b \,{\mathrm e}^{\mu x} \left ({\mathrm e}^{\lambda x} a +b \,{\mathrm e}^{\mu x}+\mu \right ) y = 0 \]

unknown

[[_2nd_order, _with_linear_symmetries]]

N/A

1.651

11103

\[ {}y^{\prime \prime }+2 k \,{\mathrm e}^{\mu x} y^{\prime }+\left (a \,{\mathrm e}^{2 \lambda x}+b \,{\mathrm e}^{\lambda x}+k^{2} {\mathrm e}^{2 \mu x}+k \mu \,{\mathrm e}^{\mu x}+c \right ) y = 0 \]

unknown

[[_2nd_order, _with_linear_symmetries]]

N/A

1.574

11104

\[ {}y^{\prime \prime }-\left (a +2 b \,{\mathrm e}^{x a}\right ) y^{\prime }+b^{2} {\mathrm e}^{2 x a} y = 0 \]

second_order_change_of_variable_on_x_method_2, second_order_change_of_variable_on_y_method_1

[[_2nd_order, _with_linear_symmetries]]

0.909

11105

\[ {}y^{\prime \prime }+\left (a \,{\mathrm e}^{2 \lambda x}+\lambda \right ) y^{\prime }-a \lambda \,{\mathrm e}^{2 \lambda x} y = 0 \]

unknown

[[_2nd_order, _with_linear_symmetries]]

N/A

1.309

11106

\[ {}y^{\prime \prime }+\left ({\mathrm e}^{\lambda x} a -\lambda \right ) y^{\prime }+b \,{\mathrm e}^{2 \lambda x} y = 0 \]

second_order_change_of_variable_on_x_method_2

[[_2nd_order, _with_linear_symmetries]]

0.789

11107

\[ {}y^{\prime \prime }+\left ({\mathrm e}^{\lambda x} a +b \right ) y^{\prime }+c \left ({\mathrm e}^{\lambda x} a +b -c \right ) y = 0 \]

unknown

[[_2nd_order, _with_linear_symmetries]]

N/A

1.085

11108

\[ {}y^{\prime \prime }+\left (a +b \,{\mathrm e}^{2 \lambda x}\right ) y^{\prime }+\lambda \left (a -\lambda -b \,{\mathrm e}^{2 \lambda x}\right ) y = 0 \]

unknown

[[_2nd_order, _with_linear_symmetries]]

N/A

0.976

11109

\[ {}y^{\prime \prime }+\left (a +b \,{\mathrm e}^{\lambda x}+b -3 \lambda \right ) y^{\prime }+a^{2} \lambda \left (b -\lambda \right ) {\mathrm e}^{2 \lambda x} y = 0 \]

unknown

[[_2nd_order, _with_linear_symmetries]]

N/A

1.493

11110

\[ {}y^{\prime \prime }+\left (2 \,{\mathrm e}^{\lambda x} a -\lambda \right ) y^{\prime }+\left (a^{2} {\mathrm e}^{2 \lambda x}+c \,{\mathrm e}^{\mu x}\right ) y = 0 \]

unknown

[[_2nd_order, _with_linear_symmetries]]

N/A

1.232

11111

\[ {}y^{\prime \prime }+\left (2 \,{\mathrm e}^{\lambda x} a +b \right ) y^{\prime }+\left (a^{2} {\mathrm e}^{2 \lambda x}+a \left (b +\lambda \right ) {\mathrm e}^{\lambda x}+c \right ) y = 0 \]

second_order_change_of_variable_on_y_method_1

[[_2nd_order, _with_linear_symmetries]]

0.825

11112

\[ {}y^{\prime \prime }+\left ({\mathrm e}^{\lambda x} a +2 b -\lambda \right ) y^{\prime }+\left (c \,{\mathrm e}^{2 \lambda x}+a b \,{\mathrm e}^{\lambda x}+b^{2}-b \lambda \right ) y = 0 \]

unknown

[[_2nd_order, _with_linear_symmetries]]

N/A

1.39

11113

\[ {}y^{\prime \prime }+\left (a \,{\mathrm e}^{x}+b \right ) y^{\prime }+\left (c \left (a -c \right ) {\mathrm e}^{2 x}+\left (a k +b c -2 c k +c \right ) {\mathrm e}^{x}+k \left (b -k \right )\right ) y = 0 \]

unknown

[[_2nd_order, _with_linear_symmetries]]

N/A

1.309

11114

\[ {}y^{\prime \prime }+\left ({\mathrm e}^{\lambda x} a +b \right ) y^{\prime }+\left (\alpha \,{\mathrm e}^{2 \lambda x}+\beta \,{\mathrm e}^{\lambda x}+\gamma \right ) y = 0 \]

unknown

[[_2nd_order, _with_linear_symmetries]]

N/A

1.314

11115

\[ {}y^{\prime \prime }+\left (2 \,{\mathrm e}^{\lambda x} a -\lambda \right ) y^{\prime }+\left (a^{2} {\mathrm e}^{2 \lambda x}+b \,{\mathrm e}^{2 \mu x}+c \,{\mathrm e}^{\mu x}+k \right ) y = 0 \]

unknown

[[_2nd_order, _with_linear_symmetries]]

N/A

1.483

11116

\[ {}y^{\prime \prime }+\left (2 \,{\mathrm e}^{\lambda x} a +b -\lambda \right ) y^{\prime }+\left (a^{2} {\mathrm e}^{2 \lambda x}+a b \,{\mathrm e}^{\lambda x}+c \,{\mathrm e}^{2 \mu x}+d \,{\mathrm e}^{\mu x}+k \right ) y = 0 \]

unknown

[[_2nd_order, _with_linear_symmetries]]

N/A

2.063

11117

\[ {}y^{\prime \prime }+\left ({\mathrm e}^{\lambda x} a +b \,{\mathrm e}^{\mu x}\right ) y^{\prime }+a \,{\mathrm e}^{\lambda x} \left (b \,{\mathrm e}^{\mu x}+\lambda \right ) y = 0 \]

unknown

[[_2nd_order, _with_linear_symmetries]]

N/A

1.641

11118

\[ {}y^{\prime \prime }+{\mathrm e}^{\lambda x} \left (a \,{\mathrm e}^{2 \mu x}+b \right ) y^{\prime }+\mu \left ({\mathrm e}^{\lambda x} \left (b -a \,{\mathrm e}^{2 \mu x}\right )-\mu \right ) y = 0 \]

unknown

[[_2nd_order, _with_linear_symmetries]]

N/A

1.911

11119

\[ {}y^{\prime \prime }+\left ({\mathrm e}^{\lambda x} a +b \,{\mathrm e}^{\mu x}+c \right ) y^{\prime }+\left (a \lambda \,{\mathrm e}^{\lambda x}+b \mu \,{\mathrm e}^{\mu x}\right ) y = 0 \]

exact linear second order ode, second_order_integrable_as_is

[[_2nd_order, _exact, _linear, _homogeneous]]

3.144

11120

\[ {}y^{\prime \prime }+\left ({\mathrm e}^{\lambda x} a +b \,{\mathrm e}^{\mu x}+c \right ) y^{\prime }+\left (a b \,{\mathrm e}^{x \left (\lambda +\mu \right )}+{\mathrm e}^{\lambda x} a c +b \mu \,{\mathrm e}^{\mu x}\right ) y = 0 \]

unknown

[[_2nd_order, _with_linear_symmetries]]

N/A

1.794

11121

\[ {}\frac {2 x y+1}{y}+\frac {\left (y-x \right ) y^{\prime }}{y^{2}} = 0 \]

exact, homogeneousTypeD2

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

1.813

11122

\[ {}\frac {y^{2}-2 x^{2}}{x y^{2}-x^{3}}+\frac {\left (2 y^{2}-x^{2}\right ) y^{\prime }}{y^{3}-x^{2} y} = 0 \]

exact, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated

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

6.898

11123

\[ {}\frac {1}{\sqrt {x^{2}+y^{2}}}+\left (\frac {1}{y}-\frac {x}{y \sqrt {x^{2}+y^{2}}}\right ) y^{\prime } = 0 \]

exact, first_order_ode_lie_symmetry_calculated

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

2.803

11124

\[ {}y+x +x y^{\prime } = 0 \]

exact, linear, differentialType, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup

[_linear]

1.278

11125

\[ {}6 x -2 y+1+\left (2 y-2 x -3\right ) y^{\prime } = 0 \]

exact, differentialType, homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated

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

4.003

11126

\[ {}\sec \left (x \right ) \cos \left (y\right )^{2}-\cos \left (x \right ) \sin \left (y\right ) y^{\prime } = 0 \]

exact, separable, first_order_ode_lie_symmetry_lookup

[_separable]

7.841

11127

\[ {}\left (1+x \right ) y^{2}-x^{3} y^{\prime } = 0 \]

exact, riccati, separable, first_order_ode_lie_symmetry_lookup

[_separable]

0.849

11128

\[ {}2 \left (1-y^{2}\right ) x y+\left (x^{2}+1\right ) \left (1+y^{2}\right ) y^{\prime } = 0 \]

exact, separable, first_order_ode_lie_symmetry_lookup

[_separable]

3.162

11129

\[ {}\sin \left (x \right ) \cos \left (y\right )^{2}+\cos \left (x \right )^{2} y^{\prime } = 0 \]

exact, separable, first_order_ode_lie_symmetry_lookup

[_separable]

2.36

11130

\[ {}x \,{\mathrm e}^{\frac {y}{x}}+y-x y^{\prime } = 0 \]

homogeneousTypeD, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup

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

1.009

11131

\[ {}2 x^{2} y+3 y^{3}-\left (x^{3}+2 x y^{2}\right ) y^{\prime } = 0 \]

homogeneousTypeD2, first_order_ode_lie_symmetry_calculated

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

3.087

11132

\[ {}y^{2}-x y+x^{2} y^{\prime } = 0 \]

riccati, bernoulli, exactByInspection, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup

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

0.946

11133

\[ {}2 x^{2} y+y^{3}-x^{3} y^{\prime } = 0 \]

bernoulli, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup

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

1.338

11134

\[ {}y^{3}+x^{3} y^{\prime } = 0 \]

exact, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup

[_separable]

1.187

11135

\[ {}x +y \cos \left (\frac {y}{x}\right )-x \cos \left (\frac {y}{x}\right ) y^{\prime } = 0 \]

homogeneousTypeD, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup

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

1.654

11136

\[ {}4 x +3 y+1+\left (1+x +y\right ) y^{\prime } = 0 \]

homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated

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

1.957

11137

\[ {}4 x -y+2+\left (x +y+3\right ) y^{\prime } = 0 \]

homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated

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

1.927

11138

\[ {}2 x +y-\left (4 x +2 y-1\right ) y^{\prime } = 0 \]

first_order_ode_lie_symmetry_calculated

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

1.305

11139

\[ {}y+2 x y^{2}-x^{2} y^{3}+2 x^{2} y y^{\prime } = 0 \]

riccati, exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated

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

1.801

11140

\[ {}2 y+3 x y^{2}+\left (x +2 x^{2} y\right ) y^{\prime } = 0 \]

exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated

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

2.91

11141

\[ {}y+x y^{2}+\left (x -x^{2} y\right ) y^{\prime } = 0 \]

exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated

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

1.565

11142

\[ {}y^{\prime }+y \cot \left (x \right ) = \sec \left (x \right ) \]

linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup

[_linear]

1.151

11143

\[ {}x y^{\prime }+\left (1+x \right ) y = {\mathrm e}^{x} \]

linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup

[_linear]

0.905

11144

\[ {}y^{\prime }-\frac {2 y}{1+x} = \left (1+x \right )^{3} \]

linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup

[_linear]

0.865

11145

\[ {}\left (x^{3}+x \right ) y^{\prime }+4 x^{2} y = 2 \]

linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup

[_linear]

0.918

11146

\[ {}x^{2} y^{\prime }+\left (1-2 x \right ) y = x^{2} \]

linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup

[_linear]

0.898

11147

\[ {}\left (-x^{2}+1\right ) y^{\prime }-2 \left (1+x \right ) y = y^{\frac {5}{2}} \]

bernoulli, first_order_ode_lie_symmetry_lookup

[_rational, _Bernoulli]

16.983

11148

\[ {}y y^{\prime }+x y^{2} = x \]

exact, bernoulli, separable, first_order_ode_lie_symmetry_lookup

[_separable]

2.46

11149

\[ {}\sin \left (y\right ) y^{\prime }+\sin \left (x \right ) \cos \left (y\right ) = \sin \left (x \right ) \]

exact, separable, first_order_ode_lie_symmetry_lookup

[_separable]

32.255

11150

\[ {}4 x y^{\prime }+3 y+{\mathrm e}^{x} x^{4} y^{5} = 0 \]

bernoulli, first_order_ode_lie_symmetry_lookup

[_Bernoulli]

1.53

11151

\[ {}y^{\prime }-\frac {y+1}{1+x} = \sqrt {y+1} \]

first_order_ode_lie_symmetry_calculated

[[_1st_order, _with_linear_symmetries]]

3.266

11152

\[ {}x^{4} y \left (3 y+2 x y^{\prime }\right )+x^{2} \left (4 y+3 x y^{\prime }\right ) = 0 \]

first_order_ode_lie_symmetry_calculated

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

9.448

11153

\[ {}y^{2} \left (3 y-6 x y^{\prime }\right )-x \left (y-2 x y^{\prime }\right ) = 0 \]

exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup

[_separable]

1.021

11154

\[ {}2 x^{3} y-y^{2}-\left (2 x^{4}+x y\right ) y^{\prime } = 0 \]

first_order_ode_lie_symmetry_calculated

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

2.711

11155

\[ {}y^{2}-x y+x^{2} y^{\prime } = 0 \]

riccati, bernoulli, exactByInspection, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup

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

0.939

11156

\[ {}\frac {-y+x y^{\prime }}{\sqrt {x^{2}-y^{2}}} = x y^{\prime } \]

exactWithIntegrationFactor

[‘y=_G(x,y’)‘]

2.869

11157

\[ {}x +y-\left (x -y\right ) y^{\prime } = 0 \]

exactByInspection, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated

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

1.5

11158

\[ {}x^{2}+y^{2}-2 x y y^{\prime } = 0 \]

bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup

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

1.666

11159

\[ {}x -y^{2}+2 x y y^{\prime } = 0 \]

bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup

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

0.887

11160

\[ {}-y+x y^{\prime } = x^{2}+y^{2} \]

riccati, exactByInspection, homogeneousTypeD2

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

1.434

11161

\[ {}3 x^{2}+6 x y+3 y^{2}+\left (2 x^{2}+3 x y\right ) y^{\prime } = 0 \]

homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated

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

3.418

11162

\[ {}2 x +\left (x^{2}+y^{2}+2 y\right ) y^{\prime } = 0 \]

exactWithIntegrationFactor

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

1.183

11163

\[ {}y^{4}+2 y+\left (x y^{3}+2 y^{4}-4 x \right ) y^{\prime } = 0 \]

exactWithIntegrationFactor

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

1.352

11164

\[ {}x^{3} y-y^{4}+\left (x y^{3}-x^{4}\right ) y^{\prime } = 0 \]

exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup

[_separable]

0.923

11165

\[ {}y^{2}-x^{2}+2 m x y+\left (m y^{2}-m \,x^{2}-2 x y\right ) y^{\prime } = 0 \]

homogeneousTypeD2, first_order_ode_lie_symmetry_calculated

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

11.212

11166

\[ {}x y^{\prime }-y+2 x^{2} y-x^{3} = 0 \]

linear, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup

[_linear]

1.48

11167

\[ {}\left (x +y\right ) y^{\prime }-1 = 0 \]

homogeneousTypeC, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup

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

0.92

11168

\[ {}x +y y^{\prime }+y-x y^{\prime } = 0 \]

exactByInspection, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated

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

1.106

11169

\[ {}x y^{\prime }-a y+b y^{2} = c \,x^{2 a} \]

riccati

[_rational, _Riccati]

1.706

11170

\[ {}x \sqrt {1-y^{2}}+y \sqrt {-x^{2}+1}\, y^{\prime } = 0 \]

exact, separable, first_order_ode_lie_symmetry_lookup

[_separable]

1.969

11171

\[ {}\sqrt {1-y^{2}}+\sqrt {-x^{2}+1}\, y^{\prime } = 0 \]

exact, separable, first_order_ode_lie_symmetry_lookup

[_separable]

1.859

11172

\[ {}y^{\prime }-x^{2} y = x^{5} \]

linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup

[_linear]

0.726

11173

\[ {}\left (y-x \right )^{2} y^{\prime } = 1 \]

first_order_ode_lie_symmetry_calculated

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

1.933

11174

\[ {}x y^{\prime }+y+x^{4} y^{4} {\mathrm e}^{x} = 0 \]

bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup

[_Bernoulli]

1.786

11175

\[ {}\left (1-x \right ) y+\left (1-y\right ) x y^{\prime } = 0 \]

exact, separable, first_order_ode_lie_symmetry_lookup

[_separable]

1.22

11176

\[ {}\left (y-x \right ) y^{\prime }+y = 0 \]

homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated

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

1.315

11177

\[ {}-y+x y^{\prime } = \sqrt {x^{2}+y^{2}} \]

first_order_ode_lie_symmetry_calculated

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

3.91

11178

\[ {}-y+x y^{\prime } = \sqrt {x^{2}-y^{2}} \]

first_order_ode_lie_symmetry_calculated

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

1.668

11179

\[ {}x \sin \left (\frac {y}{x}\right )-y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime } = 0 \]

homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated

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

2.359

11180

\[ {}x -2 y+5+\left (4+2 x -y\right ) y^{\prime } = 0 \]

homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated

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

3.618

11181

\[ {}y^{\prime }+\frac {y}{\left (-x^{2}+1\right )^{\frac {3}{2}}} = \frac {x +\sqrt {-x^{2}+1}}{\left (-x^{2}+1\right )^{2}} \]

linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup

[_linear]

5.35

11182

\[ {}\left (-x^{2}+1\right ) y^{\prime }-x y = a x y^{2} \]

exact, riccati, bernoulli, separable, first_order_ode_lie_symmetry_lookup

[_separable]

3.538

11183

\[ {}x y^{2} \left (3 y+x y^{\prime }\right )-2 y+x y^{\prime } = 0 \]

exactByInspection, first_order_ode_lie_symmetry_calculated

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

3.125

11184

\[ {}\left (x^{2}+1\right ) y^{\prime }+y = \arctan \left (x \right ) \]

linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup

[_linear]

0.999

11185

\[ {}5 x y-3 y^{3}+\left (3 x^{2}-7 x y^{2}\right ) y^{\prime } = 0 \]

exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated

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

2.938

11186

\[ {}y^{\prime }+y \cos \left (x \right ) = \frac {\sin \left (2 x \right )}{2} \]

linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup

[_linear]

1.682

11187

\[ {}x y^{2}+y-x y^{\prime } = 0 \]

riccati, bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup

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

0.929

11188

\[ {}\left (1-x \right ) y-\left (y+1\right ) x y^{\prime } = 0 \]

exact, separable, first_order_ode_lie_symmetry_lookup

[_separable]

1.126

11189

\[ {}3 x^{2} y+\left (x^{3}+x^{3} y^{2}\right ) y^{\prime } = 0 \]

exact, separable, first_order_ode_lie_symmetry_lookup

[_separable]

1.99

11190

\[ {}\left (x^{2}+y^{2}\right ) \left (x +y y^{\prime }\right ) = \left (x^{2}+y^{2}+x \right ) \left (-y+x y^{\prime }\right ) \]

unknown

[_rational]

N/A

1.308

11191

\[ {}2 x +3 y-1+\left (2 x +3 y-5\right ) y^{\prime } = 0 \]

first_order_ode_lie_symmetry_calculated

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

1.217

11192

\[ {}y^{3}-2 x^{2} y+\left (2 x y^{2}-x^{3}\right ) y^{\prime } = 0 \]

homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated

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

4.365

11193

\[ {}2 x^{3} y^{2}-y+\left (2 x^{2} y^{3}-x \right ) y^{\prime } = 0 \]

exactWithIntegrationFactor

[_rational]

1.448

11194

\[ {}\left (x^{2}+y^{2}\right ) \left (x +y y^{\prime }\right )+\sqrt {1+x^{2}+y^{2}}\, \left (y-x y^{\prime }\right ) = 0 \]

first_order_ode_lie_symmetry_calculated

[[_1st_order, _with_linear_symmetries]]

2.616

11195

\[ {}1+{\mathrm e}^{\frac {y}{x}}+{\mathrm e}^{\frac {x}{y}} \left (1-\frac {x}{y}\right ) y^{\prime } = 0 \]

homogeneousTypeD2, first_order_ode_lie_symmetry_calculated

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

2.179

11196

\[ {}x y^{\prime }+y-y^{2} \ln \left (x \right ) = 0 \]

riccati, bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup

[_Bernoulli]

1.163

11197

\[ {}x^{3} y^{4}+x^{2} y^{3}+x y^{2}+y+\left (x^{4} y^{3}-x^{3} y^{2}-x^{3} y+x \right ) y^{\prime } = 0 \]

unknown

[_rational]

N/A

1.693

11198

\[ {}\left (2 \sqrt {x y}-x \right ) y^{\prime }+y = 0 \]

first_order_ode_lie_symmetry_calculated

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

3.38

11199

\[ {}{y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+x y = 0 \]

quadrature

[_quadrature]

0.577

11200

\[ {}x {y^{\prime }}^{2}-2 y y^{\prime }-x = 0 \]

dAlembert

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

0.416