6.207 Problems 20601 to 20700

Table 6.413: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

20601

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

20602

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

20603

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

20604

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

20605

\[ {} y^{\prime \prime \prime }-\frac {4 y^{\prime \prime }}{x}+\frac {5 y^{\prime }}{x^{2}}-\frac {2 y}{x^{3}} = 1 \]

20606

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

20607

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

20608

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

20609

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

20610

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

20611

\[ {} x^{2} y^{\prime \prime }+7 x y^{\prime }+5 y = x^{5} \]

20612

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

20613

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

20614

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

20615

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

20616

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

20617

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

20618

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

20619

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

20620

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

20621

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

20622

\[ {} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+8 x y^{\prime }+2 y = x^{2}+3 x -4 \]

20623

\[ {} x^{2} y^{\prime \prime }+2 x y^{\prime }-20 y = \left (1+x \right )^{2} \]

20624

\[ {} -8 y+7 x y^{\prime }-3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime } = x^{2}+\frac {1}{x^{2}} \]

20625

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

20626

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

20627

\[ {} x^{2} y^{\prime \prime }-3 x y^{\prime }+5 y = x^{2} \sin \left (\ln \left (x \right )\right ) \]

20628

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

20629

\[ {} y+3 x y^{\prime }+9 x^{2} y^{\prime \prime }+6 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime } = \left (\ln \left (x \right )+1\right )^{2} \]

20630

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

20631

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

20632

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

20633

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

20634

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

20635

\[ {} x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+8 x y^{\prime }+2 y = x^{2}+3 x -4 \]

20636

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

20637

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

20638

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

20639

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

20640

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

20641

\[ {} \left (2 x^{2}+3 x \right ) y^{\prime \prime }+\left (6 x +3\right ) y^{\prime }+2 y = {\mathrm e}^{x} \left (1+x \right ) \]

20642

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

20643

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

20644

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

20645

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

20646

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

20647

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

20648

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

20649

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

20650

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

20651

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

20652

\[ {} y^{\prime \prime } = x \,{\mathrm e}^{x} \]

20653

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

20654

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

20655

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

20656

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

20657

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

20658

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

20659

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

20660

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

20661

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

20662

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

20663

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

20664

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

20665

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

20666

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

20667

\[ {} y^{\prime \prime }+y^{\prime } = {\mathrm e}^{x} \]

20668

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

20669

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

20670

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

20671

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

20672

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

20673

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

20674

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

20675

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

20676

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

20677

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

20678

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

20679

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

20680

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

20681

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

20682

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

20683

\[ {} 1+{y^{\prime }}^{2}+y y^{\prime \prime } = 0 \]

20684

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

20685

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

20686

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

20687

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

20688

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

20689

\[ {} a y^{\prime \prime } = \sqrt {1+{y^{\prime }}^{2}} \]

20690

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

20691

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

20692

\[ {} y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0 \]

20693

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

20694

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

20695

\[ {} y^{\left (5\right )}-n^{2} y^{\prime \prime \prime } = {\mathrm e}^{a x} \]

20696

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

20697

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

20698

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

20699

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

20700

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