4.24.42 Problems 4101 to 4200

Table 4.1435: Second or higher order ODE with non-constant coefficients

#

ODE

Mathematica

Maple

Sympy

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

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

16674

\[ {} x^{2} y^{\prime \prime }-5 x y^{\prime }+29 y = 0 \]

16675

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

16676

\[ {} x^{2} y^{\prime \prime }+5 x y^{\prime }+29 y = 0 \]

16677

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

16678

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

16679

\[ {} 4 x^{2} y^{\prime \prime }+37 y = 0 \]

16680

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

16681

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }-25 y = 0 \]

16682

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

16683

\[ {} 3 x^{2} y^{\prime \prime }-7 x y^{\prime }+3 y = 0 \]

16684

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

16685

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

16686

\[ {} x^{2} y^{\prime \prime }-11 x y^{\prime }+36 y = 0 \]

16687

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

16688

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

16689

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

16690

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

16691

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

16692

\[ {} x^{3} y^{\prime \prime \prime }-5 x^{2} y^{\prime \prime }+14 x y^{\prime }-18 y = 0 \]

16693

\[ {} -8 y+7 x y^{\prime }-3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime } = 0 \]

16694

\[ {} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+15 x^{2} y^{\prime \prime }+9 x y^{\prime }+16 y = 0 \]

16695

\[ {} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }-9 x y^{\prime }+9 y = 0 \]

16696

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

16697

\[ {} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+7 x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \]

16706

\[ {} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 10 x +12 \]

16712

\[ {} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 1 \]

16713

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

16714

\[ {} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 22 x +24 \]

16715

\[ {} x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y = x^{2} \]

16716

\[ {} x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y = x \]

16717

\[ {} x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y = 1 \]

16718

\[ {} x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y = 4 x^{2}+2 x +3 \]

16792

\[ {} x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y = \frac {5}{x^{3}} \]

16793

\[ {} 2 x^{2} y^{\prime \prime }-x y^{\prime }+y = \frac {50}{x^{3}} \]

16794

\[ {} 2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = 85 \cos \left (2 \ln \left (x \right )\right ) \]

16795

\[ {} x^{2} y^{\prime \prime }-2 y = 15 \cos \left (3 \ln \left (x \right )\right )-10 \sin \left (3 \ln \left (x \right )\right ) \]

16796

\[ {} 3 x^{2} y^{\prime \prime }-7 x y^{\prime }+3 y = 4 x^{3} \]

16797

\[ {} 2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = \frac {10}{x} \]

16798

\[ {} x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 6 x^{3} \]

16799

\[ {} x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = 64 x^{2} \ln \left (x \right ) \]

16800

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

16806

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

16807

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }-9 y = 12 x^{3} \]

16808

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

16809

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

16810

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

16811

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

16812

\[ {} x y^{\prime \prime }+\left (2 x +2\right ) y^{\prime }+2 y = 8 \,{\mathrm e}^{2 x} \]

16813

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

16814

\[ {} x^{2} y^{\prime \prime }-2 x y^{\prime }-4 y = \frac {10}{x} \]

16817

\[ {} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = x^{3} \]

16818

\[ {} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = {\mathrm e}^{-x^{2}} \]

16821

\[ {} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }-9 x y^{\prime }+9 y = 12 x \sin \left (x^{2}\right ) \]

16824

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

16827

\[ {} 16 y-7 x y^{\prime }+x^{2} y^{\prime \prime } = 0 \]

16828

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

16832

\[ {} x^{2} y^{\prime \prime }+7 x y^{\prime }+9 y = 0 \]

16833

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

16835

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

16837

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

16838

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

16840

\[ {} x^{2} y^{\prime \prime }+2 x y^{\prime }-30 y = 0 \]

16843

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

16845

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

16846

\[ {} 9 x^{2} y^{\prime \prime }+3 x y^{\prime }+y = 0 \]

16850

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

16856

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }-9 y = 3 \sqrt {x} \]

16859

\[ {} x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 18 \ln \left (x \right ) \]

16861

\[ {} 2 x^{2} y^{\prime \prime }-x y^{\prime }-2 y = 10 x^{2} \]

16863

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

16864

\[ {} x^{2} y^{\prime \prime }+3 x y^{\prime }+2 y = 6 \]

16865

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

16870

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

16871

\[ {} x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \frac {1}{x} \]

16885

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

17072

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

17073

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

17074

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

17087

\[ {} x^{2} y^{\prime \prime }-12 x y^{\prime }+42 y = 0 \]

17088

\[ {} t^{2} y^{\prime \prime }+3 t y^{\prime }+5 y = 0 \]

17113

\[ {} t^{2} y^{\prime \prime }-12 t y^{\prime }+42 y = 0 \]

17114

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

17133

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

17134

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

17145

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

17288

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

17466

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

17470

\[ {} 3 t^{2} y^{\prime \prime }-5 t y^{\prime }-3 y = 0 \]

17471

\[ {} t^{2} y^{\prime \prime }+7 t y^{\prime }-7 y = 0 \]

17476

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

17483

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

17484

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

17485

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

17486

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

17488

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