4.4.29 Problems 2801 to 2900

Table 4.471: Second ODE homogeneous ODE

#

ODE

Mathematica

Maple

Sympy

13681

\[ {} 4 x^{\prime \prime }-20 x^{\prime }+21 x = 0 \]

13682

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

13683

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

13684

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

13685

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

13705

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

13706

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

13707

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

13708

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

13709

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

13710

\[ {} \tan \left (t \right ) x^{\prime \prime }-3 x^{\prime }+\left (\tan \left (t \right )+3 \cot \left (t \right )\right ) x = 0 \]

13717

\[ {} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \]

13718

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

13719

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

13720

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

13721

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

13722

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

13723

\[ {} 4 t^{2} x^{\prime \prime }+8 t x^{\prime }+5 x = 0 \]

13724

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

13725

\[ {} 3 x^{2} z^{\prime \prime }+5 x z^{\prime }-z = 0 \]

13726

\[ {} t^{2} x^{\prime \prime }+3 t x^{\prime }+13 x = 0 \]

13727

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

13827

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

13836

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\left (9 x^{2}-\frac {1}{25}\right ) y = 0 \]

13838

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

13840

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

13841

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

13842

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

13848

\[ {} m x^{\prime \prime } = f \left (x\right ) \]

13849

\[ {} m x^{\prime \prime } = f \left (x^{\prime }\right ) \]

13853

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

13857

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

13861

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

13863

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

13864

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

13879

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

13898

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

13901

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

13903

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

13906

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

13907

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

13911

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

13912

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

13913

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

13914

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

13915

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

13918

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

13919

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

13921

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

13922

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

13928

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

13930

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

13932

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

13933

\[ {} \left (x^{2}+2 x \right ) y^{\prime \prime }+\left (x^{2}+x +10\right ) y^{\prime } = \left (25-6 x \right ) y \]

13934

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

13935

\[ {} \left (x^{2}-x \right ) y^{\prime \prime }+\left (2 x^{2}+4 x -3\right ) y^{\prime }+8 x y = 0 \]

13937

\[ {} \left (2 \sin \left (x \right )-\cos \left (x \right )\right ) y^{\prime \prime }+\left (7 \sin \left (x \right )+4 \cos \left (x \right )\right ) y^{\prime }+10 \cos \left (x \right ) y = 0 \]

13940

\[ {} y^{\prime \prime }+9 y = 0 \]

13941

\[ {} 4 y^{\prime \prime }-4 y^{\prime }+5 y = 0 \]

13942

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

13943

\[ {} y^{\prime \prime }-4 y^{\prime }+5 y = 0 \]

13944

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

13945

\[ {} 4 y^{\prime \prime }-4 y^{\prime }+37 y = 0 \]

13946

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

13947

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

13948

\[ {} 4 y^{\prime \prime }-12 y^{\prime }+13 y = 0 \]

13949

\[ {} y^{\prime \prime }+4 y^{\prime }+13 y = 0 \]

13950

\[ {} y^{\prime \prime }+6 y^{\prime }+9 y = 0 \]

13952

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

13953

\[ {} y^{\prime \prime }-20 y^{\prime }+51 y = 0 \]

13954

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

13955

\[ {} 3 y^{\prime \prime }+8 y^{\prime }-3 y = 0 \]

13956

\[ {} 2 y^{\prime \prime }+20 y^{\prime }+51 y = 0 \]

13957

\[ {} 4 y^{\prime \prime }+40 y^{\prime }+101 y = 0 \]

13958

\[ {} y^{\prime \prime }+6 y^{\prime }+34 y = 0 \]

14051

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

14052

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

14057

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

14058

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

14067

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

14068

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

14069

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

14070

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

14071

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

14072

\[ {} y^{\prime \prime }+\beta y^{\prime }+\gamma y = 0 \]

14073

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

14081

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

14082

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

14147

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

14149

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

14150

\[ {} y^{\prime \prime } = \frac {a}{y^{3}} \]

14152

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

14155

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

14158

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

14159

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

14160

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

14161

\[ {} y^{\prime \prime }+12 y = 7 y^{\prime } \]

14162

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

14163

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

14164

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