4.4.37 Problems 3601 to 3700

Table 4.487: Second ODE homogeneous ODE

#

ODE

Mathematica

Maple

Sympy

18539

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

18576

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

18577

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

18604

\[ {} e y^{\prime \prime } = P \left (-y+a \right ) \]

18615

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

18621

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

18622

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

18623

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

18630

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

18631

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

18645

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

18646

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

18647

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

18788

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

18789

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

18790

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

18791

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

18794

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

18852

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

18853

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

18870

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

18873

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

18874

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

18878

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

18879

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

18880

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

18881

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

18883

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

18886

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

18888

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

18889

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

18894

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

18895

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

18903

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

18908

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

18910

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

18912

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

18915

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

18919

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

18920

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

18926

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

18927

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

18928

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

18930

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

18931

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

18932

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

18933

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

18934

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

18935

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

18938

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

18939

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

18940

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

18941

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

18942

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

18943

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

18944

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

18945

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

18947

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

18949

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

18952

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

18953

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

18954

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

18956

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

18967

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

19080

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

19082

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

19083

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

19084

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

19086

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

19236

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

19244

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

19266

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

19268

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

19270

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

19274

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

19275

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

19278

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

19279

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

19280

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

19295

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

19297

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

19298

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

19299

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

19300

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

19301

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

19302

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

19304

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

19309

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

19314

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

19316

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

19317

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

19318

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

19320

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

19321

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

19325

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

19329

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

19336

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

19337

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

19338

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

19339

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