2.127 Problems 12601 to 12700

Table 2.253: Main lookup table

#

ODE

Mathematica result

Maple result

12601

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

12602

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

12603

\[ {}\theta ^{\prime } = \frac {9}{10}-\frac {11 \cos \left (\theta \right )}{10} \]

12604

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

12605

\[ {}\theta ^{\prime } = \frac {11}{10}-\frac {9 \cos \left (\theta \right )}{10} \]

12606

\[ {}v^{\prime } = -\frac {v}{R C} \]

12607

\[ {}v^{\prime } = \frac {K -v}{R C} \]

12608

\[ {}v^{\prime } = 2 V \left (t \right )-2 v \]

12609

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

12610

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

12611

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

12612

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

12613

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

12614

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

12615

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

12616

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

12617

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

12618

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

12619

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

12620

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

12621

\[ {}\theta ^{\prime } = \frac {9}{10}-\frac {11 \cos \left (\theta \right )}{10} \]

12622

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

12623

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

12624

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

12625

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

12626

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

12627

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

12628

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

12629

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

12630

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

12631

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

12632

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

12633

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

12634

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

12635

\[ {}y^{\prime } = y^{2}-4 y-12 \]

12636

\[ {}y^{\prime } = y^{2}-4 y-12 \]

12637

\[ {}y^{\prime } = y^{2}-4 y-12 \]

12638

\[ {}y^{\prime } = y^{2}-4 y-12 \]

12639

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

12640

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

12641

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

12642

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

12643

\[ {}w^{\prime } = w \cos \left (w\right ) \]

12644

\[ {}w^{\prime } = w \cos \left (w\right ) \]

12645

\[ {}w^{\prime } = w \cos \left (w\right ) \]

12646

\[ {}w^{\prime } = w \cos \left (w\right ) \]

12647

\[ {}w^{\prime } = w \cos \left (w\right ) \]

12648

\[ {}w^{\prime } = \left (1-w\right ) \sin \left (w\right ) \]

12649

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

12650

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

12651

\[ {}w^{\prime } = 3 w^{3}-12 w^{2} \]

12652

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

12653

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

12654

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

12655

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

12656

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

12657

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

12658

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

12659

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

12660

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

12661

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

12662

\[ {}y^{\prime } = y \cos \left (\frac {\pi y}{2}\right ) \]

12663

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

12664

\[ {}y^{\prime } = y \sin \left (\frac {\pi y}{2}\right ) \]

12665

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

12666

\[ {}y^{\prime } = \cos \left (\frac {\pi y}{2}\right ) \]

12667

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

12668

\[ {}y^{\prime } = y \sin \left (\frac {\pi y}{2}\right ) \]

12669

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

12670

\[ {}y^{\prime } = -4 y+9 \,{\mathrm e}^{-t} \]

12671

\[ {}y^{\prime } = -4 y+3 \,{\mathrm e}^{-t} \]

12672

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

12673

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

12674

\[ {}y^{\prime } = 3 y-4 \,{\mathrm e}^{3 t} \]

12675

\[ {}y^{\prime } = \frac {y}{2}+4 \,{\mathrm e}^{\frac {t}{2}} \]

12676

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

12677

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

12678

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

12679

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

12680

\[ {}y^{\prime }-2 y = 7 \,{\mathrm e}^{2 t} \]

12681

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

12682

\[ {}y^{\prime }+2 y = t^{2}+2 t +1+{\mathrm e}^{4 t} \]

12683

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

12684

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

12685

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

12686

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

12687

\[ {}y^{\prime } = \frac {3 y}{t}+t^{5} \]

12688

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

12689

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

12690

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

12691

\[ {}y^{\prime }-\frac {2 y}{t} = t^{3} {\mathrm e}^{t} \]

12692

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

12693

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

12694

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

12695

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

12696

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

12697

\[ {}y^{\prime }-\frac {3 y}{t} = 2 t^{3} {\mathrm e}^{2 t} \]

12698

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

12699

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

12700

\[ {}y^{\prime } = \frac {y}{t^{2}}+4 \cos \left (t \right ) \]