4.1.29 Problems 2801 to 2900

Table 4.57: First order ode

#

ODE

Mathematica

Maple

Sympy

6825

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

6826

\[ {} y^{\prime } = \frac {2 x +y-1}{4 x +2 y+5} \]

6827

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

6828

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

6829

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

6830

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

6831

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

6832

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

6833

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

6834

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

6835

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

6836

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

6837

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

6838

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

6839

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

6840

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

6841

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

6842

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

6843

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

6844

\[ {} \left (7 x +5 y\right ) y^{\prime }+10 x +8 y = 0 \]

6845

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

6846

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

6847

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

6848

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

6849

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

6850

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

6851

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

6852

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

6853

\[ {} 3 z^{2} z^{\prime }-a z^{3} = 1+x \]

6854

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

6855

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

6856

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

6857

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

6858

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

6859

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

6860

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

6861

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

6862

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

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

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

6866

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

6867

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

6868

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

6869

\[ {} \left (7 x +5 y\right ) y^{\prime }+10 x +8 y = 0 \]

6870

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

6871

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

6872

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

6873

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

6874

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

6875

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

6876

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

6877

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

6878

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

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

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

6882

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

6883

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

6884

\[ {} \frac {\sqrt {f \,x^{4}+c \,x^{3}+c \,x^{2}+b x +a}\, y^{\prime }}{\sqrt {a +b y+c y^{2}+c y^{3}+f y^{4}}} = -1 \]

6885

\[ {} {y^{\prime }}^{2}-5 y^{\prime }+6 = 0 \]

6886

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

6887

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

6888

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

6889

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

6890

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

6891

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

6892

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

6893

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

6894

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

6895

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

6896

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

6897

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

6898

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

6899

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

6900

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

6901

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

6902

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

6903

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

6904

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

6905

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

6906

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

6907

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

6908

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

6909

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

6910

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

6911

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

6912

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

6913

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

6914

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

6915

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

6916

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

6917

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

6918

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

6919

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

6920

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

6921

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

6922

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

6923

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

6924

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