4.26.25 Problems 2401 to 2500

Table 4.1539: Second order, Linear, Homogeneous and non-constant coefficients

#

ODE

Mathematica

Maple

Sympy

14956

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

14957

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

14958

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

14963

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

14964

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

14965

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

14966

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

15065

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

15066

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

15067

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

15068

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

15069

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

15070

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

15077

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

15078

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

15079

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

15080

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

15081

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

15082

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

15083

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

15084

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

15085

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

15086

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

15196

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

15200

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

15213

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

15239

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

15266

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

15267

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

15271

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

15272

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

15274

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

15275

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

15278

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

15279

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

15281

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

15282

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

15292

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

15293

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

15294

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

15295

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

15297

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

15411

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

15412

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

15417

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

15418

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

15427

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

15428

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

15429

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

15433

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

15447

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

15448

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

15597

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

15599

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

15601

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

15607

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

15614

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

15615

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

15616

\[ {} x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 0 \]

15632

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

15633

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

15634

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

15635

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

15636

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

15637

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

15775

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

15779

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

16275

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

16497

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

16500

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

16501

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

16531

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

16550

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

16551

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

16561

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

16562

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

16563

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

16564

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

16565

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

16566

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

16568

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

16569

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

16570

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

16571

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

16572

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

16587

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

16588

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

16589

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

16590

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

16591

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

16592

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

16593

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

16666

\[ {} x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y = 0 \]

16667

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

16668

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

16669

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

16670

\[ {} x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 0 \]

16671

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

16672

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

16673

\[ {} x^{2} y^{\prime \prime }-19 x y^{\prime }+100 y = 0 \]