3.4.12 Problems 1101 to 1200

Table 3.359: Second ODE homogeneous ODE

#

ODE

Mathematica

Maple

7840

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

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

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

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

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

7852

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

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

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

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

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

7900

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

7901

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

7902

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

7903

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

7904

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

7905

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

7906

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

7907

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

7908

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

7909

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

7910

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

7911

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

7912

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

7913

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

7914

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

7915

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

7916

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

7917

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

7918

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

7919

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

7920

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

7921

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

7922

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

7923

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

7924

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

7925

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

7926

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

7927

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

7928

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

7929

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

7930

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

7931

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

7932

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

7933

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

7934

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

7935

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

7936

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

7937

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

7938

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

7939

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