6.137 Problems 13601 to 13700

Table 6.273: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

13601

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

13602

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

13603

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

13604

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

13605

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

13606

\[ {} -\frac {6 y^{\prime } x}{\left (3 x^{2}+1\right )^{2}}+\frac {y^{\prime \prime }}{3 x^{2}+1}+\lambda \left (3 x^{2}+1\right ) y = 0 \]

13607

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

13608

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

13609

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

13610

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

13611

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

13612

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

13613

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

13614

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

13615

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

13616

\[ {} [x^{\prime }\left (t \right ) = a x \left (t \right )+b y \left (t \right ), y^{\prime }\left (t \right ) = c x \left (t \right )+d y \left (t \right )] \]

13617

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

13618

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

13619

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

13620

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

13621

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

13622

\[ {} x^{\prime \prime }+\left (5 x^{4}-6 x^{2}\right ) x^{\prime }+x^{3} = 0 \]

13623

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

13624

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

13625

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

13626

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

13627

\[ {} u^{\prime } = 4 t \ln \left (t \right ) \]

13628

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

13629

\[ {} T^{\prime } = {\mathrm e}^{-t} \sin \left (2 t \right ) \]

13630

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

13631

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

13632

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

13633

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

13634

\[ {} x^{\prime } {\mathrm e}^{3 t}+3 x \,{\mathrm e}^{3 t} = {\mathrm e}^{-t} \]

13635

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

13636

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

13637

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

13638

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

13639

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

13640

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

13641

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

13642

\[ {} x^{\prime } = t^{2} x \]

13643

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

13644

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

13645

\[ {} x^{\prime }+p x = q \]

13646

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

13647

\[ {} i^{\prime } = p \left (t \right ) i \]

13648

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

13649

\[ {} m v^{\prime } = -m g +k v^{2} \]

13650

\[ {} x^{\prime } = k x-x^{2} \]

13651

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

13652

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

13653

\[ {} x^{\prime }+t x = 4 t \]

13654

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

13655

\[ {} y^{\prime }+{\mathrm e}^{-x} y = 1 \]

13656

\[ {} x^{\prime }+x \tanh \left (t \right ) = 3 \]

13657

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

13658

\[ {} x^{\prime }+5 x = t \]

13659

\[ {} x^{\prime }+\left (a +\frac {1}{t}\right ) x = b \]

13660

\[ {} T^{\prime } = -k \left (T-\mu -a \cos \left (\omega \left (t -\phi \right )\right )\right ) \]

13661

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

13662

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

13663

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

13664

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

13665

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

13666

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

13667

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

13668

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

13669

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

13670

\[ {} x^{\prime } = k x-x^{2} \]

13671

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

13672

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

13673

\[ {} z^{\prime \prime }-4 z^{\prime }+13 z = 0 \]

13674

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

13675

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

13676

\[ {} \theta ^{\prime \prime }+4 \theta = 0 \]

13677

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

13678

\[ {} 2 z^{\prime \prime }+7 z^{\prime }-4 z = 0 \]

13679

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

13680

\[ {} x^{\prime \prime }+6 x^{\prime }+10 x = 0 \]

13681

\[ {} 4 x^{\prime \prime }-20 x^{\prime }+21 x = 0 \]

13682

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

13683

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

13684

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

13685

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

13686

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

13687

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

13688

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

13689

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

13690

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

13691

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

13692

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

13693

\[ {} x^{\prime \prime }+2 x^{\prime }+10 x = {\mathrm e}^{-t} \]

13694

\[ {} x^{\prime \prime }+2 x^{\prime }+10 x = {\mathrm e}^{-t} \cos \left (3 t \right ) \]

13695

\[ {} x^{\prime \prime }+6 x^{\prime }+10 x = {\mathrm e}^{-2 t} \cos \left (t \right ) \]

13696

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

13697

\[ {} x^{\prime \prime }+x^{\prime }-2 x = 12 \,{\mathrm e}^{-t}-6 \,{\mathrm e}^{t} \]

13698

\[ {} x^{\prime \prime }+4 x = 289 t \,{\mathrm e}^{t} \sin \left (2 t \right ) \]

13699

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

13700

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