2.79 Problems 7801 to 7900

Table 2.79: Main lookup table

#

ODE

Mathematica result

Maple result

7801

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

7802

\[ {}\left (2 y+x +7\right ) y^{\prime }-y+2 x +4 = 0 \]

7803

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

7804

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

7805

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

7806

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

7807

\[ {}\left (4 y-3 x -5\right ) y^{\prime }-3 y+7 x +2 = 0 \]

7808

\[ {}\left (4 y+11 x -11\right ) y^{\prime }-25 y-8 x +62 = 0 \]

7809

\[ {}\left (12 y-5 x -8\right ) y^{\prime }-5 y+2 x +3 = 0 \]

7810

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

7811

\[ {}\left (a y+b x +c \right ) y^{\prime }+\alpha y+\beta x +\gamma = 0 \]

7812

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

7813

\[ {}x y y^{\prime }-y^{2}+a \,x^{3} \cos \relax (x ) = 0 \]

7814

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

7815

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

7816

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

7817

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

7818

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

7819

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

7820

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

7821

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

7822

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

7823

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

7824

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

7825

\[ {}\left (2 x y+4 x^{3}\right ) y^{\prime }+y^{2}+112 x^{2} y = 0 \]

7826

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

7827

\[ {}\left (2+3 x \right ) \left (y-2 x -1\right ) y^{\prime }-y^{2}+x y-7 x^{2}-9 x -3 = 0 \]

7828

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

7829

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

7830

\[ {}\left (B x y+A \,x^{2}+a x +b y+c \right ) y^{\prime }-B g \relax (x )^{2}+A x y+\alpha x +\beta y+\gamma = 0 \]

7831

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

7832

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

7833

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

7834

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

7835

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

7836

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

7837

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

7838

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

7839

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

7840

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

7841

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

7842

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

7843

\[ {}2 x^{3}+y y^{\prime }+3 x^{2} y^{2}+7 = 0 \]

7844

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

7845

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

7846

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

7847

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

7848

\[ {}f \relax (x ) y y^{\prime }+g \relax (x ) y^{2}+h \relax (x ) = 0 \]

7849

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

7850

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

7851

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

7852

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

7853

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

7854

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

7855

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

7856

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

7857

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

7858

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

7859

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

7860

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

7861

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

7862

\[ {}\left (y+3 x -1\right )^{2} y^{\prime }-\left (2 y-1\right ) \left (4 y+6 x -3\right ) = 0 \]

7863

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

7864

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

7865

\[ {}\left (4 y^{2}+2 x y+3 x^{2}\right ) y^{\prime }+y^{2}+6 x y+2 x^{2} = 0 \]

7866

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

7867

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

7868

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

7869

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

7870

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

7871

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

7872

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

7873

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

7874

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

7875

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

7876

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

7877

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

7878

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

7879

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

7880

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

7881

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

7882

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

7883

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

7884

\[ {}\left (10 x^{3} y^{2}+x^{2} y+2 x \right ) y^{\prime }+5 x^{2} y^{3}+x y^{2} = 0 \]

7885

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

7886

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

7887

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

7888

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

7889

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

7890

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

7891

\[ {}\left (20 y^{3}-3 x y^{2}+6 x^{2} y+3 x^{3}\right ) y^{\prime }-y^{3}+6 x y^{2}+9 x^{2} y+4 x^{3} = 0 \]

7892

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

7893

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

7894

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

7895

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

7896

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

7897

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

7898

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

7899

\[ {}\left (7 x y^{3}+y-5 x \right ) y^{\prime }+y^{4}-5 y = 0 \]

7900

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