4.3.62 Problems 6101 to 6200

Table 4.407: Second order ode

#

ODE

Mathematica

Maple

Sympy

18624

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

18627

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

18628

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

18629

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

18630

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

18631

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

18632

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

18633

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

18634

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

18635

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

18638

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

18639

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

18653

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

18654

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

18655

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

18796

\[ {} y^{\prime \prime }+3 y^{\prime }-54 y = 0 \]

18797

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

18798

\[ {} 2 y^{\prime \prime }+5 y^{\prime }-12 y = 0 \]

18799

\[ {} 9 y^{\prime \prime }+18 y^{\prime }-16 y = 0 \]

18802

\[ {} y^{\prime \prime }+8 y^{\prime }+25 y = 0 \]

18805

\[ {} y^{\prime \prime }-5 y^{\prime }+6 y = {\mathrm e}^{4 x} \]

18806

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

18807

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

18811

\[ {} y^{\prime \prime }-2 y^{\prime }+y = 3 \,{\mathrm e}^{\frac {5 x}{2}} \]

18815

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

18816

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

18819

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

18820

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

18821

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

18822

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

18826

\[ {} y^{\prime \prime }+4 y = \sin \left (3 x \right )+{\mathrm e}^{x}+x^{2} \]

18827

\[ {} y^{\prime \prime }-5 y^{\prime }+6 y = x +{\mathrm e}^{m x} \]

18828

\[ {} y^{\prime \prime }-y a^{2} = {\mathrm e}^{a x}+{\mathrm e}^{n x} \]

18834

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

18835

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

18836

\[ {} y^{\prime \prime }+n^{2} y = x^{4} {\mathrm e}^{x} \]

18840

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

18842

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

18846

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

18847

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

18849

\[ {} y^{\prime \prime }-9 y^{\prime }+20 y = 20 x \]

18852

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

18853

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

18856

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

18857

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

18858

\[ {} x^{2} y^{\prime \prime }+2 x y^{\prime }-20 y = \left (1+x \right )^{2} \]

18859

\[ {} x^{2} y^{\prime \prime }+7 x y^{\prime }+5 y = x^{5} \]

18860

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

18861

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

18863

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

18865

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

18869

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

18870

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

18873

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

18874

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

18875

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

18877

\[ {} x^{5} y^{\prime \prime }+3 x^{3} y^{\prime }+\left (3-6 x \right ) x^{2} y = x^{4}+2 x -5 \]

18878

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

18879

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

18880

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

18881

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

18882

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

18885

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

18886

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

18887

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

18888

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

18889

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

18891

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

18892

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

18894

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

18895

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

18896

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

18897

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

18901

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

18902

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

18903

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

18911

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

18912

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

18916

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

18918

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

18919

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

18920

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

18922

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

18923

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

18925

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

18927

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

18928

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

18929

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

18931

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

18932

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

18933

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

18934

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

18935

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

18936

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

18937

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

18938

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

18939

\[ {} 4 x^{2} y^{\prime \prime }+4 x^{5} y^{\prime }+\left (x^{8}+6 x^{4}+4\right ) y = 0 \]

18940

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

18941

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

18942

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