4.26.28 Problems 2701 to 2800

Table 4.1545: Second order, Linear, Homogeneous and non-constant coefficients

#

ODE

Mathematica

Maple

Sympy

19894

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

19901

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

19902

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

19904

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

19979

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

19994

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

19995

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

20009

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

20010

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

20216

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

20217

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

20234

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

20259

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

20276

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

20283

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

20290

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

20291

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

20292

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

20294

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

20295

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

20296

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

20297

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

20298

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

20299

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

20302

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

20303

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

20304

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

20305

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

20306

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

20307

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

20308

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

20309

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

20311

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

20313

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

20316

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

20317

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

20320

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

20331

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

20600

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

20608

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

20630

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

20632

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

20634

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

20638

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

20639

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

20643

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

20644

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

20665

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

20668

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

20711

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

20720

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

20723

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

20728

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

20729

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

20730

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

20731

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

20732

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

20733

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

20735

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

20736

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

20738

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

20739

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

20740

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

20741

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

20742

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

20744

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

20745

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

20746

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

20747

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

20748

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

20749

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

20750

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

20751

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

20752

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

20753

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

20764

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

20767

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

20768

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

20770

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

20771

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

20772

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

20776

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

20778

\[ {} \left (x^{3}-2 x^{2}\right ) y^{\prime \prime }+2 x^{2} y^{\prime }-12 \left (x -2\right ) y = 0 \]

20780

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

20781

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }-9 y = 0 \]

20782

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

20783

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

20786

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

20791

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

20894

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

20898

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

20899

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

20903

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

20905

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

20906

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

20907

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

20908

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

20911

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

20917

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

20957

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