5.3.18 Problems 1701 to 1800

Table 5.81: Problems not solved by Sympy

#

ODE

Mathematica

Maple

Sympy

6674

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

6675

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

6676

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

6681

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

6682

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

6683

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

6684

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

6685

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

6686

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

6687

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

6688

\[ {} a \,x^{2} y-6 y^{\prime }+x^{2} y^{\prime \prime \prime } = 0 \]

6690

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

6693

\[ {} a \,x^{2} y+6 y^{\prime }+6 x y^{\prime \prime }+x^{2} y^{\prime \prime \prime } = 0 \]

6694

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

6695

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

6696

\[ {} 10 y^{\prime }+8 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime \prime } = 0 \]

6697

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

6698

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

6701

\[ {} y+x y^{\prime }+\left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime \prime }+x \left (\operatorname {b0} x +\operatorname {a0} \right ) y^{\prime \prime \prime } = f \left (x \right ) \]

6714

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

6716

\[ {} -2 \left (x^{2}+4\right ) y+x \left (x^{2}+8\right ) y^{\prime }-4 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime } = 0 \]

6717

\[ {} -\left (-a \,x^{3}+12\right ) y+6 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime } = 0 \]

6718

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

6719

\[ {} 6 y+18 x y^{\prime }+9 x^{2} y^{\prime \prime }+\left (x^{3}+1\right ) y^{\prime \prime \prime } = 0 \]

6720

\[ {} -12 y+3 \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (x^{2}+1\right ) y^{\prime \prime \prime } = 0 \]

6721

\[ {} -4 y-14 x y^{\prime }+\left (-8 x^{2}+3\right ) y^{\prime \prime }+x \left (-x^{2}+1\right ) y^{\prime \prime \prime } = 0 \]

6722

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

6723

\[ {} -8 y+3 y^{\prime } \left (1+x \right )+\left (1+x \right )^{2} y^{\prime \prime }+\left (1+x \right )^{3} y^{\prime \prime \prime } = 0 \]

6724

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

6726

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

6729

\[ {} 10 x^{2} y^{\prime }+8 x^{3} y^{\prime \prime }+x^{2} \left (x^{2}+1\right ) y^{\prime \prime \prime } = -1+3 x^{2}+2 x^{2} \ln \left (x \right ) \]

6730

\[ {} -4 \left (3 x +1\right ) y+2 x \left (5 x +2\right ) y^{\prime }-2 x^{2} \left (2 x +1\right ) y^{\prime \prime }+x^{3} \left (1+x \right ) y^{\prime \prime \prime } = 0 \]

6732

\[ {} -4 \left (3 x^{2}+1\right ) y+2 x \left (5 x^{2}+2\right ) y^{\prime }-2 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x^{3} \left (x^{2}+1\right ) y^{\prime \prime \prime } = 0 \]

6733

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

6734

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

6757

\[ {} 10 f^{\prime }\left (x \right ) y^{\prime }+3 y \left (3 f \left (x \right )^{2}+f^{\prime \prime }\left (x \right )\right )+10 f \left (x \right ) y^{\prime \prime }+y^{\prime \prime \prime \prime } = 0 \]

6760

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

6761

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

6769

\[ {} a^{4} x^{4} y+4 a^{3} x^{3} y^{\prime }+6 a^{2} x^{2} y^{\prime \prime }+4 a x y^{\prime \prime \prime }+y^{\prime \prime \prime \prime } = 0 \]

6779

\[ {} -a^{2} y+12 y^{\prime \prime }+8 x y^{\prime \prime \prime }+x^{2} y^{\prime \prime \prime \prime } = 0 \]

6781

\[ {} -c^{4} y+16 \left (1+a -b \right ) \left (2+a -b \right ) y^{\prime \prime }+32 \left (2+a -b \right ) x y^{\prime \prime \prime }+16 x^{2} y^{\prime \prime \prime \prime } = 0 \]

6782

\[ {} -a^{4} x^{3} y-x y^{\prime \prime }+2 x^{2} y^{\prime \prime \prime }+x^{3} y^{\prime \prime \prime \prime } = 0 \]

6784

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

6788

\[ {} a y+12 x^{2} y^{\prime \prime }+8 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime } = 0 \]

6789

\[ {} \operatorname {A4} y+\operatorname {A3} x y^{\prime }+\operatorname {A2} \,x^{2} y^{\prime \prime }+\operatorname {A1} \,x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime } = 0 \]

6790

\[ {} -b^{4} x^{\frac {2}{a}} y+16 \left (-2 a +1\right ) \left (1-a \right ) a^{2} x^{2} y^{\prime \prime }-32 \left (-2 a +1\right ) a^{2} x^{3} y^{\prime \prime \prime }+16 a^{4} x^{4} y^{\prime \prime \prime \prime } = 0 \]

6791

\[ {} y \,{\mathrm e}^{x}+4 \,{\mathrm e}^{x} y^{\prime }+6 \,{\mathrm e}^{x} y^{\prime \prime }+4 \left ({\mathrm e}^{x}+2\right ) y^{\prime \prime \prime }+\left ({\mathrm e}^{x}+2 x \right ) y^{\prime \prime \prime \prime } = 0 \]

6800

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

6801

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

6802

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

6803

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

6804

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

6805

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

6806

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

6807

\[ {} 3 y^{2}+18 y y^{\prime } x +9 x^{2} {y^{\prime }}^{2}+9 x^{2} y y^{\prime \prime }+3 x^{3} y^{\prime } y^{\prime \prime }+x^{3} y y^{\prime \prime \prime } = 0 \]

6808

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

6809

\[ {} 15 {y^{\prime }}^{3}-18 y y^{\prime } y^{\prime \prime }+4 y^{2} y^{\prime \prime \prime } = 0 \]

6810

\[ {} 40 {y^{\prime }}^{3}-45 y y^{\prime } y^{\prime \prime }+9 y^{2} y^{\prime \prime \prime } = 0 \]

6811

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

6812

\[ {} y^{\prime } y^{\prime \prime } = a x {y^{\prime }}^{5}+3 {y^{\prime \prime }}^{2} \]

6813

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

6814

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

6815

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

6816

\[ {} {y^{\prime }}^{3} y^{\prime \prime \prime } = 1 \]

6817

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

6818

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

6819

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

6820

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

6822

\[ {} 3 y^{\prime \prime } y^{\prime \prime \prime \prime } = 5 {y^{\prime \prime \prime }}^{2} \]

6823

\[ {} 40 {y^{\prime \prime \prime }}^{3}-45 y^{\prime \prime } y^{\prime \prime \prime } y^{\prime \prime \prime \prime }+9 {y^{\prime \prime }}^{2} y^{\left (5\right )} = 0 \]

6829

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

6832

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

6845

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

6849

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

6860

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

6863

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

6864

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

6865

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

6872

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

6877

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

6879

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

6880

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

6881

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

6883

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

6897

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

6900

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

6901

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

6906

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

6915

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

6917

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

6924

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

6930

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

6932

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

6934

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

6935

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

6936

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

6937

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

6939

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

6940

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

6941

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