6.237 Problems 23601 to 23700

Table 6.473: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

23601

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

23602

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

23603

\[ {} y^{\left (6\right )}-3 y^{\prime \prime \prime \prime } = 1 \]

23604

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

23605

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

23606

\[ {} 4 y+y^{\prime \prime } = 4 x^{3}-8 x^{2}-14 x +7 \]

23607

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

23608

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

23609

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

23610

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

23611

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

23612

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

23613

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

23614

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

23615

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

23616

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

23617

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

23618

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

23619

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

23620

\[ {} 6 y-5 y^{\prime }+y^{\prime \prime } = {\mathrm e}^{x} \sin \left (x \right ) \]

23621

\[ {} y^{\prime \prime }-7 y^{\prime }-8 y = {\mathrm e}^{x} \left (x^{2}+2\right ) \]

23622

\[ {} y^{\prime \prime }-5 y^{\prime }+4 y = {\mathrm e}^{2 x} \cos \left (x \right )+{\mathrm e}^{2 x} \sin \left (x \right ) \]

23623

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

23624

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

23625

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

23626

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

23627

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

23628

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

23629

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

23630

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

23631

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

23632

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

23633

\[ {} 4 y^{\prime \prime }+7 y^{\prime }+3 y = 5 \cos \left (t \right ) \]

23634

\[ {} e i u^{\prime \prime \prime \prime } = \cos \left (x \right ) \]

23635

\[ {} e i u^{\prime \prime \prime \prime } = {\mathrm e}^{-x} \]

23636

\[ {} e i u^{\prime \prime \prime \prime } = \sinh \left (x \right ) \]

23637

\[ {} e i u^{\prime \prime \prime \prime } = 1 \]

23638

\[ {} e i u^{\prime \prime \prime \prime } = x^{2} \]

23639

\[ {} e i u^{\prime \prime \prime \prime } = x^{4} \]

23640

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

23641

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

23642

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

23643

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

23644

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

23645

\[ {} y^{\prime \prime }+10 y^{\prime }+25 y = \frac {{\mathrm e}^{-5 x} \ln \left (x \right )}{x^{2}} \]

23646

\[ {} y^{\prime \prime }+6 y^{\prime }+9 y = \frac {{\mathrm e}^{-3 x}}{x^{3}} \]

23647

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

23648

\[ {} y^{\prime \prime }-12 y^{\prime }+36 y = {\mathrm e}^{6 x} \ln \left (x \right ) \]

23649

\[ {} 5 y+4 y^{\prime }+y^{\prime \prime } = {\mathrm e}^{-2 x} \sec \left (x \right ) \]

23650

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

23651

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

23652

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

23653

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

23654

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

23655

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

23656

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

23657

\[ {} 2 x^{2} y^{\prime \prime }+7 x y^{\prime }-3 y = \frac {\ln \left (x \right )}{x^{2}} \]

23658

\[ {} x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = \ln \left (x \right ) \left (\frac {1}{x^{3}}+\frac {1}{x^{5}}\right ) \]

23659

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

23660

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

23661

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

23662

\[ {} y^{\prime \prime }+6 y^{\prime }+9 y = \frac {{\mathrm e}^{-3 x}}{x^{3}} \]

23663

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

23664

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

23665

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

23666

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

23667

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

23668

\[ {} y^{\left (5\right )}-y^{\prime }-\frac {4 y}{x} = 0 \]

23669

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

23670

\[ {} x^{\prime \prime }+2 x^{\prime }+x = -\frac {{\mathrm e}^{-t}}{\left (t +1\right )^{2}} \]

23671

\[ {} [x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )+6 x_{2} \left (t \right )] \]

23672

\[ {} [x_{1}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )+4 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+3 x_{2} \left (t \right )] \]

23673

\[ {} \left [x_{1}^{\prime }\left (t \right ) = 2 \sin \left (t \right ) x_{1} \left (t \right )+\ln \left (t \right ) x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = \frac {x_{1} \left (t \right )}{t -2}+\frac {{\mathrm e}^{t} x_{2} \left (t \right )}{t +1}\right ] \]

23674

\[ {} [x^{\prime }\left (t \right ) = 5 x \left (t \right )-6 y \left (t \right )+1, y^{\prime }\left (t \right ) = 6 x \left (t \right )-7 y \left (t \right )+1] \]

23675

\[ {} [x^{\prime }\left (t \right ) = 5 x \left (t \right )-6 y \left (t \right ), y^{\prime }\left (t \right ) = 6 x \left (t \right )-7 y \left (t \right )] \]

23676

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

23677

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

23678

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

23679

\[ {} [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )] \]

23680

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

23681

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

23682

\[ {} \left [x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+\left (1-t \right ) x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = \frac {x_{1} \left (t \right )}{t}-x_{2} \left (t \right )\right ] \]

23683

\[ {} [x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right )-x_{3} \left (t \right )+x_{4} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -x_{2} \left (t \right )+x_{4} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{3} \left (t \right )-x_{4} \left (t \right ), x_{4}^{\prime }\left (t \right ) = 2 x_{4} \left (t \right )] \]

23684

\[ {} [x_{1}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )+2 x_{2} \left (t \right )+2 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+2 x_{2} \left (t \right )-4 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-4 x_{2} \left (t \right )+2 x_{3} \left (t \right )] \]

23685

\[ {} [x_{1}^{\prime }\left (t \right ) = -10 x_{1} \left (t \right )+x_{2} \left (t \right )+7 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -9 x_{1} \left (t \right )+4 x_{2} \left (t \right )+5 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -17 x_{1} \left (t \right )+x_{2} \left (t \right )+12 x_{3} \left (t \right )] \]

23686

\[ {} [x_{1}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )-x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )] \]

23687

\[ {} [x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )] \]

23688

\[ {} [x_{1}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )-x_{2} \left (t \right )+3 \,{\mathrm e}^{2 t}, x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )+2 t] \]

23689

\[ {} [x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-2 x_{2} \left (t \right )+1, x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+t] \]

23690

\[ {} [x^{\prime }\left (t \right ) = 5 x \left (t \right )-6 y \left (t \right )+1, y^{\prime }\left (t \right ) = 6 x \left (t \right )-7 y \left (t \right )+1] \]

23691

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

23692

\[ {} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right )+2 t^{2}, y^{\prime }\left (t \right ) = 5 x \left (t \right )+y \left (t \right )-1] \]

23693

\[ {} [x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+x_{2} \left (t \right )] \]

23694

\[ {} [N_{1}^{\prime }\left (t \right ) = 4 N_{1} \left (t \right )-6 N_{2} \left (t \right ), N_{2}^{\prime }\left (t \right ) = 8 N_{1} \left (t \right )-10 N_{2} \left (t \right )] \]

23695

\[ {} [x_{1}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )-x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )] \]

23696

\[ {} [x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )] \]

23697

\[ {} [x_{1}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )-x_{2} \left (t \right )+3 \,{\mathrm e}^{2 t}, x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )+2 t] \]

23698

\[ {} [x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-2 x_{2} \left (t \right )+1, x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+t] \]

23699

\[ {} [x^{\prime }\left (t \right ) = 5 x \left (t \right )-6 y \left (t \right )+1, y^{\prime }\left (t \right ) = 6 x \left (t \right )-7 y \left (t \right )+1] \]

23700

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