4.26.26 Problems 2501 to 2600

Table 4.1541: Second order, Linear, Homogeneous and non-constant coefficients

#

ODE

Mathematica

Maple

Sympy

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

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

16824

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

16827

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

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

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

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

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

16885

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

17072

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

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

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

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

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

17489

\[ {} 4 t^{2} y^{\prime \prime }+4 t y^{\prime }+\left (36 t^{2}-1\right ) y = 0 \]

17490

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

17491

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

17527

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

17528

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

17646

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

17648

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

17650

\[ {} 4 t^{2} y^{\prime \prime }+4 t y^{\prime }+\left (16 t^{2}-1\right ) y = 0 \]

17727

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

17728

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

17729

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

17730

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

17731

\[ {} 4 x^{2} y^{\prime \prime }+17 y = 0 \]

17732

\[ {} 9 x^{2} y^{\prime \prime }-9 x y^{\prime }+10 y = 0 \]

17733

\[ {} 2 x^{2} y^{\prime \prime }-2 x y^{\prime }+20 y = 0 \]

17734

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

17735

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

17736

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

17737

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

17738

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

17757

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

17758

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

17759

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

17760

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

17769

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

17770

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

17771

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

17776

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

17778

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

17780

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

17781

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

17782

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

17783

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

17785

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

17786

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

17793

\[ {} 6 x^{2} y^{\prime \prime }+5 x y^{\prime }-y = 0 \]

17848

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

17849

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

17890

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

17893

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

17894

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

17895

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

17896

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

17897

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

17898

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

17899

\[ {} x^{2} y^{\prime \prime }-7 x y^{\prime }+25 y = 0 \]

18207

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

18208

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

18209

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

18211

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

18404

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

18405

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

18406

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

18407

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

18408

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