4.26.23 Problems 2201 to 2300

Table 4.1157: Second order, Linear, Homogeneous and non-constant coefficients

#

ODE

Mathematica

Maple

Sympy

18182

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

18184

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

18187

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

18192

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

18195

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

18196

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

18197

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

18198

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

18199

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

18200

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

18201

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

18202

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

18203

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

18204

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

18205

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

18206

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

18207

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

18208

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

18233

\[ {} x^{2} y^{\prime \prime }+3 x y^{\prime }+10 y = 0 \]

18234

\[ {} 2 x^{2} y^{\prime \prime }+10 x y^{\prime }+8 y = 0 \]

18235

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

18236

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

18237

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

18238

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

18239

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

18240

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

18241

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }-16 y = 0 \]

18242

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

18243

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

18335

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

18379

\[ {} x y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }-\left (4 x +9\right ) y = 0 \]

18381

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

18434

\[ {} t^{2} x^{\prime \prime }-6 t x^{\prime }+12 x = 0 \]

18437

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

18454

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

18455

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

18523

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

18529

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

18536

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

18537

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

18539

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

18615

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

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

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

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

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

18895

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

18912

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

18919

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

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

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

18956

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

18967

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

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

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

19279

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

19280

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

19301

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

19304

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

19348

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

19357

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

19360

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

19365

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

19366

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

19367

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

19368

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

19369

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

19370

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

19372

\[ {} 4 x^{2} y^{\prime \prime }+4 x^{5} y^{\prime }+\left (x^{3}+6 x^{2}+4\right ) y = 0 \]

19373

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

19375

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

19376

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

19377

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