4.24.43 Problems 4201 to 4300

Table 4.1437: Second or higher order ODE with non-constant coefficients

#

ODE

Mathematica

Maple

Sympy

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

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

17535

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

17536

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

17641

\[ {} t^{2} y^{\prime \prime }+3 t y^{\prime }+y = \ln \left (t \right ) \]

17642

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

17643

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

17646

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

17647

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

17648

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

17649

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

17650

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

17651

\[ {} 4 t^{2} y^{\prime \prime }+4 t y^{\prime }+\left (16 t^{2}-1\right ) y = 16 t^{{3}/{2}} \]

17652

\[ {} t^{2} \left (\ln \left (t \right )-1\right ) y^{\prime \prime }-t y^{\prime }+y = -\frac {3 \left (1+\ln \left (t \right )\right )}{4 \sqrt {t}} \]

17653

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

17692

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

17723

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

17724

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

17725

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

17726

\[ {} t y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime } = \frac {45}{8 t^{{7}/{2}}} \]

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

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

17739

\[ {} x^{3} y^{\prime \prime \prime }+22 x^{2} y^{\prime \prime }+124 x y^{\prime }+140 y = 0 \]

17740

\[ {} x^{3} y^{\prime \prime \prime }-4 x^{2} y^{\prime \prime }-46 x y^{\prime }+100 y = 0 \]

17741

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

17742

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

17743

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

17744

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

17745

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

17746

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

17747

\[ {} x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = \frac {1}{x^{5}} \]

17748

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

17749

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

17750

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

17751

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

17752

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }-16 y = \ln \left (x \right ) \]

17753

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

17754

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

17755

\[ {} x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-11 x y^{\prime }+16 y = \frac {1}{x^{3}} \]

17756

\[ {} x^{3} y^{\prime \prime \prime }+16 x^{2} y^{\prime \prime }+70 x y^{\prime }+80 y = \frac {1}{x^{13}} \]

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

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

17761

\[ {} x^{3} y^{\prime \prime \prime }+10 x^{2} y^{\prime \prime }-20 x y^{\prime }+20 y = 0 \]

17762

\[ {} x^{3} y^{\prime \prime \prime }+15 x^{2} y^{\prime \prime }+54 x y^{\prime }+42 y = 0 \]

17763

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

17764

\[ {} x^{3} y^{\prime \prime \prime }-6 x^{2} y^{\prime \prime }+17 x y^{\prime }-17 y = 0 \]

17765

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

17766

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

17767

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

17768

\[ {} 9 x^{2} y^{\prime \prime }+27 x y^{\prime }+10 y = \frac {1}{x} \]

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

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

17772

\[ {} x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }+37 x y^{\prime } = 0 \]

17773

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

17774

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

17775

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

17776

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

17777

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

17778

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

17779

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

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

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

17784

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

17785

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

17786

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

17787

\[ {} x^{3} y^{\prime \prime \prime }+16 x^{2} y^{\prime \prime }+79 x y^{\prime }+125 y = 0 \]

17788

\[ {} x^{4} y^{\prime \prime \prime \prime }+5 x^{3} y^{\prime \prime \prime }-12 x^{2} y^{\prime \prime }-12 x y^{\prime }+48 y = 0 \]

17789

\[ {} x^{4} y^{\prime \prime \prime \prime }+14 x^{3} y^{\prime \prime \prime }+55 x^{2} y^{\prime \prime }+65 x y^{\prime }+15 y = 0 \]

17790

\[ {} x^{4} y^{\prime \prime \prime \prime }+8 x^{3} y^{\prime \prime \prime }+27 x^{2} y^{\prime \prime }+35 x y^{\prime }+45 y = 0 \]

17791

\[ {} x^{4} y^{\prime \prime \prime \prime }+10 x^{3} y^{\prime \prime \prime }+27 x^{2} y^{\prime \prime }+21 x y^{\prime }+4 y = 0 \]

17792

\[ {} x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+44 x y^{\prime }+58 y = 0 \]

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

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