2.79 Problems 7801 to 7900

Table 2.157: Main lookup table

#

ODE

Mathematica result

Maple result

7801

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

7802

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

7803

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

7804

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

7805

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

7806

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

7807

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

7808

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

7809

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

7810

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

7811

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

7812

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

7813

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

7814

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

7815

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

7816

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

7817

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

7818

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

7819

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (36 x^{2}-\frac {1}{4}\right ) y = 0 \]

7820

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

7821

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

7822

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

7823

\[ {}16 x^{2} y^{\prime \prime }+32 x y^{\prime }+\left (x^{4}-12\right ) y = 0 \]

7824

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

7825

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

7826

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

7827

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

7828

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

7829

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+30 y = 0 \]

7830

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

7831

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

7832

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

7833

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

7834

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

7835

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

7836

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

7837

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

7838

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

7839

\[ {}2 \left (t^{2}-5 t +6\right ) y^{\prime \prime }+\left (2 t -3\right ) y^{\prime }-8 y = 0 \]

7840

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

7841

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

7842

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

7843

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

7844

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

7845

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

7846

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

7847

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

7848

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

7849

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

7850

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

7851

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

7852

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

7853

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

7854

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

7855

\[ {}y^{\prime \prime }+\frac {y}{2 x^{4}} = 0 \]

7856

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

7857

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

7858

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

7859

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

7860

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

7861

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

7862

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

7863

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

7864

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

7865

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

7866

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

7867

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

7868

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

7869

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

7870

\[ {}2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (11 x^{2}+11 x +9\right ) y^{\prime }+\left (7 x^{2}+10 x +6\right ) y = 0 \]

7871

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

7872

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

7873

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

7874

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

7875

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

7876

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

7877

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

7878

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

7879

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

7880

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

7881

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

7882

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

7883

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

7884

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

7885

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

7886

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

7887

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

7888

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

7889

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

7890

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

7891

\[ {}\left (x^{2}-1\right ) y^{\prime \prime }-6 x y^{\prime }+12 y = 0 \]

7892

\[ {}\left (x^{2}+3\right ) y^{\prime \prime }-7 x y^{\prime }+16 y = 0 \]

7893

\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+8 x y^{\prime }+12 y = 0 \]

7894

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

7895

\[ {}5 y^{\prime \prime }-2 x y^{\prime }+10 y = 0 \]

7896

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

7897

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

7898

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

7899

\[ {}\left (x^{2}-6 x +10\right ) y^{\prime \prime }-4 \left (-3+x \right ) y^{\prime }+6 y = 0 \]

7900

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