5.3.13 Problems 1201 to 1300

Table 5.59: Problems not solved by Sympy

#

ODE

Mathematica

Maple

Sympy

6725

\[ {} y^{\prime \prime }-4 y^{\prime }+3 y = \frac {1}{1+{\mathrm e}^{-x}} \]

6753

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

6754

\[ {} \left (2 x +1\right )^{2} y^{\prime \prime }-2 \left (2 x +1\right ) y^{\prime }-12 y = 6 x \]

6755

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

6756

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

6757

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

6758

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

6759

\[ {} y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }-10 y = 0 \]

6760

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

6761

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

6762

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

6764

\[ {} x^{4} y^{\prime \prime }+2 x^{3} y^{\prime }+y = \frac {1+x}{x} \]

6765

\[ {} x^{8} y^{\prime \prime }+4 x^{7} y^{\prime }+y = \frac {1}{x^{3}} \]

6766

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

6768

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

6770

\[ {} x y^{\prime \prime }+2 y^{\prime }+4 x y = 4 \]

6771

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

6776

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

6777

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

6778

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

6779

\[ {} \left (2 x -3\right ) y^{\prime \prime \prime }-\left (6 x -7\right ) y^{\prime \prime }+4 x y^{\prime }-4 y = 8 \]

6780

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

6781

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

6782

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

6783

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

6784

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

6785

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

6786

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

6790

\[ {} [x^{\prime }\left (t \right )-x \left (t \right )+y^{\prime }\left (t \right )+3 y \left (t \right ) = {\mathrm e}^{-t}-1, x^{\prime }\left (t \right )+2 x \left (t \right )+y^{\prime }\left (t \right )+3 y \left (t \right ) = {\mathrm e}^{2 t}+1] \]

6793

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

6801

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

6810

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

6816

\[ {} x^{3} \left (1+x \right ) y^{\prime \prime \prime }-\left (2+4 x \right ) x^{2} y^{\prime \prime }+\left (4+10 x \right ) x y^{\prime }-\left (4+12 x \right ) y = 0 \]

6817

\[ {} x^{3} \left (x^{2}+1\right ) y^{\prime \prime \prime }-\left (4 x^{2}+2\right ) x^{2} y^{\prime \prime }+\left (10 x^{2}+4\right ) x y^{\prime }-\left (12 x^{2}+4\right ) y = 0 \]

6818

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

6821

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

6833

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

6837

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

6838

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}+\frac {9}{4}\right ) y = 0 \]

6839

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}+\frac {25}{4}\right ) y = 0 \]

6843

\[ {} x^{3} y^{\prime \prime }+y = \frac {1}{x^{4}} \]

6844

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

6845

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

6856

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

6857

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

6858

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

6859

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

6862

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

6864

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

6869

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

6871

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

6873

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

6876

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

6877

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

6878

\[ {} t^{5} y^{\prime \prime \prime \prime }-t^{3} y^{\prime \prime }+6 y = 0 \]

6879

\[ {} u^{\prime \prime }+u^{\prime }+u = \cos \left (r +u\right ) \]

6880

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

6882

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

6884

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

6919

\[ {} {y^{\prime }}^{2} = 9-y^{2} \]

6921

\[ {} {y^{\prime }}^{2}-2 y^{\prime }+4 y = 4 x -1 \]

6948

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

6957

\[ {} y^{\prime } = \sqrt {y^{2}-9} \]

6960

\[ {} y^{\prime } = \sqrt {y^{2}-9} \]

6961

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

6965

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

6971

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

6976

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

6978

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

6979

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

6981

\[ {} y^{\prime } = x \sqrt {y} \]

6993

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

6995

\[ {} y^{\prime } = 6 \sqrt {y}+5 x^{3} \]

7002

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

7006

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

7014

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

7015

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

7016

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

7017

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

7018

\[ {} y^{\prime } = {\mathrm e}^{-\frac {x y^{2}}{100}} \]

7019

\[ {} y^{\prime } = {\mathrm e}^{-\frac {x y^{2}}{100}} \]

7020

\[ {} y^{\prime } = {\mathrm e}^{-\frac {x y^{2}}{100}} \]

7021

\[ {} y^{\prime } = {\mathrm e}^{-\frac {x y^{2}}{100}} \]

7047

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

7048

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

7089

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

7101

\[ {} y^{\prime } = y^{2}-4 \]

7102

\[ {} y^{\prime } = y^{2}-4 \]

7103

\[ {} y^{\prime } = y^{2}-4 \]

7104

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

7105

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

7109

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

7133

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

7138

\[ {} y^{\prime } = -\frac {8 x +5}{3 y^{2}+1} \]

7139

\[ {} y^{\prime } = -\frac {8 x +5}{3 y^{2}+1} \]

7140

\[ {} y^{\prime } = -\frac {8 x +5}{3 y^{2}+1} \]

7141

\[ {} y^{\prime } = -\frac {8 x +5}{3 y^{2}+1} \]

7143

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

7144

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

7159

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