6.186 Problems 18501 to 18600

Table 6.371: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

18501

\[ {} \theta ^{\prime \prime }-p^{2} \theta = 0 \]

18502

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

18503

\[ {} y^{\prime \prime }+12 y = 7 y^{\prime } \]

18504

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

18505

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

18506

\[ {} v^{\prime \prime }-6 v^{\prime }+13 v = {\mathrm e}^{-2 u} \]

18507

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

18508

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

18509

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

18510

\[ {} x^{\prime \prime \prime \prime }-6 x^{\prime \prime \prime }+11 x^{\prime \prime }-6 x^{\prime } = {\mathrm e}^{-3 t} \]

18511

\[ {} x^{4} y^{\prime \prime \prime \prime }+x^{3} y^{\prime \prime \prime }-20 x^{2} y^{\prime \prime }+20 x y^{\prime } = 17 x^{6} \]

18512

\[ {} t^{4} x^{\prime \prime \prime \prime }-2 t^{3} x^{\prime \prime \prime }-20 t^{2} x^{\prime \prime }+12 t x^{\prime }+16 x = \cos \left (3 \ln \left (t \right )\right ) \]

18513

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

18514

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

18515

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

18516

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

18517

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

18518

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

18519

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

18520

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

18521

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

18522

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

18523

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

18524

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

18525

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

18526

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

18527

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

18528

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

18529

\[ {} v^{\prime \prime }+\frac {2 v^{\prime }}{r} = 0 \]

18530

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

18531

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

18532

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

18533

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

18534

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

18535

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

18536

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

18537

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

18538

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

18539

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

18540

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

18541

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

18542

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

18543

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

18544

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

18545

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

18546

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

18547

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

18548

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

18549

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

18550

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

18551

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

18552

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

18553

\[ {} y \sqrt {x^{2}-1}+x \sqrt {-1+y^{2}}\, y^{\prime } = 0 \]

18554

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

18555

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

18556

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

18557

\[ {} x^{3}-3 x^{2} y+5 x y^{2}-7 y^{3}+\left (y^{4}+2 y^{2}-x^{3}+5 x^{2} y-21 x y^{2}\right ) y^{\prime } = 0 \]

18558

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

18559

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

18560

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

18561

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

18562

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

18563

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

18564

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

18565

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

18566

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

18567

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

18568

\[ {} \left (3 x +2 y-7\right ) y^{\prime } = 2 x -3 y+6 \]

18569

\[ {} \left (6 x -5 y+4\right ) y^{\prime } = 2 x -y+1 \]

18570

\[ {} \left (5 x -2 y+7\right ) y^{\prime } = x -3 y+2 \]

18571

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

18572

\[ {} \left (x -3 y+4\right ) y^{\prime } = 2 x -6 y+7 \]

18573

\[ {} \left (5 x -2 y+7\right ) y^{\prime } = 10 x -4 y+6 \]

18574

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

18575

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

18576

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

18577

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

18578

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

18579

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

18580

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

18581

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

18582

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

18583

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

18584

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

18585

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

18586

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

18587

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

18588

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

18589

\[ {} y^{\prime \prime \prime }+5 y^{\prime \prime }+6 y^{\prime } = x \]

18590

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = x \]

18591

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

18592

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

18593

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

18594

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

18595

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

18596

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

18597

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

18598

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

18599

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

18600

\[ {} e y^{\prime \prime } = \frac {w \left (\frac {L^{2}}{4}-x^{2}\right )}{2} \]