5.3.11 Problems 1001 to 1100

Table 5.55: Problems not solved by Sympy

#

ODE

Mathematica

Maple

Sympy

5654

\[ {} 3 {y^{\prime }}^{5}-y y^{\prime }+1 = 0 \]

5658

\[ {} {y^{\prime }}^{6}+f \left (x \right ) \left (y-a \right )^{5} \left (y-b \right )^{4} = 0 \]

5659

\[ {} x^{2} \left ({y^{\prime }}^{6}+3 y^{4}+3 y^{2}+1\right ) = a^{2} \]

5666

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

5667

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

5670

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

5671

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

5672

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

5673

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

5674

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

5675

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

5676

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

5677

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

5678

\[ {} {\mathrm e}^{y^{\prime }-y}-{y^{\prime }}^{2}+1 = 0 \]

5686

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

5687

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

5688

\[ {} \ln \left (\cos \left (y^{\prime }\right )\right )+y^{\prime } \tan \left (y^{\prime }\right ) = y \]

5694

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

5697

\[ {} y = x y^{\prime }+\frac {a y^{\prime }}{\sqrt {1+{y^{\prime }}^{2}}} \]

5710

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

5714

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

5725

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

5726

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

5728

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

5729

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

5730

\[ {} \frac {x^{n} y^{\prime }}{b y^{2}-c \,x^{2 a}}-\frac {a y x^{a -1}}{b y^{2}-c \,x^{2 a}}+x^{a -1} = 0 \]

5737

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

5742

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

5744

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

5745

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

5746

\[ {} u^{\prime }+u^{2} = \frac {c}{x^{{4}/{3}}} \]

5748

\[ {} u^{\prime }-u^{2} = \frac {2}{x^{{8}/{3}}} \]

5753

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

5762

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

5765

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

5766

\[ {} y y^{\prime }+x = a \sqrt {1+{y^{\prime }}^{2}} \]

5771

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

5780

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

5782

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

5789

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

5795

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

5797

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

5799

\[ {} 3 x^{2} y+8 x y^{2}+\left (x^{3}+8 x^{2} y+12 y^{2}\right ) y^{\prime } = 0 \]

5800

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

5801

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

5802

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

5804

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

5805

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

5806

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

5807

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

5808

\[ {} 4 x^{3}-\sin \left (x \right )+y^{3}-\left (y^{2}+1-3 x y^{2}\right ) y^{\prime } = 0 \]

5811

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

5816

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

5820

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

5821

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

5823

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

5824

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

5826

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

5827

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

5828

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

5830

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

5832

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

5833

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

5836

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

5838

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

5863

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

5875

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

5877

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

5884

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

5888

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

5895

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

5898

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

5901

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

5910

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

5912

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

5913

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

5995

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

5997

\[ {} y y^{\prime \prime } = {y^{\prime }}^{2}-1 \]

6000

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

6004

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

6006

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

6007

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

6010

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

6011

\[ {} y^{\prime \prime } = {\mathrm e}^{y} y^{\prime } \]

6012

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

6013

\[ {} 2 y^{\prime \prime } = {\mathrm e}^{y} \]

6016

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

6017

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

6018

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

6019

\[ {} -a y^{3}-\frac {b}{x^{{3}/{2}}}+y^{\prime } = 0 \]

6021

\[ {} y^{\prime }-x^{a} y^{3}+3 y^{2}-x^{-a} y-x^{-2 a}+a \,x^{-a -1} = 0 \]

6022

\[ {} y^{\prime }-\left (y-f \left (x \right )\right ) \left (y-g \left (x \right )\right ) \left (y-\frac {a f \left (x \right )+b g \left (x \right )}{a +b}\right ) h \left (x \right )-\frac {f^{\prime }\left (x \right ) \left (y-g \left (x \right )\right )}{f \left (x \right )-g \left (x \right )}-\frac {g^{\prime }\left (x \right ) \left (y-f \left (x \right )\right )}{g \left (x \right )-f \left (x \right )} = 0 \]

6023

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

6024

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

6027

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

6030

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

6035

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

6040

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

6042

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

6043

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