6.185 Problems 18401 to 18500

Table 6.369: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

18401

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

18402

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

18403

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

18404

\[ {} [x^{\prime }\left (t \right ) = 5 x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = -17 x \left (t \right )-5 y \left (t \right )] \]

18405

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

18406

\[ {} [x^{\prime }\left (t \right ) = 4 x \left (t \right )-3 y \left (t \right ), y^{\prime }\left (t \right ) = 8 x \left (t \right )-6 y \left (t \right )] \]

18407

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

18408

\[ {} x^{\prime \prime }+\left (5 x^{4}-9 x^{2}\right ) x^{\prime }+x^{5} = 0 \]

18409

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

18410

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

18411

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

18412

\[ {} x^{\prime } = \frac {1}{\sqrt {t^{2}+1}} \]

18413

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

18414

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

18415

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

18416

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

18417

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

18418

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

18419

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

18420

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

18421

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

18422

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

18423

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

18424

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

18425

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

18426

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

18427

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

18428

\[ {} x^{\prime }+x \tan \left (t \right ) = 0 \]

18429

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

18430

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

18431

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

18432

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

18433

\[ {} t x^{\prime }+x g \left (t \right ) = h \left (t \right ) \]

18434

\[ {} t^{2} x^{\prime \prime }-6 t x^{\prime }+12 x = 0 \]

18435

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

18436

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

18437

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

18438

\[ {} x^{\prime \prime }-5 x^{\prime }+6 x = 0 \]

18439

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

18440

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

18441

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

18442

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

18443

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

18444

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

18445

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

18446

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

18447

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

18448

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

18449

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

18450

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

18451

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

18452

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

18453

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

18454

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

18455

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

18456

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

18457

\[ {} v^{\prime \prime } = \left (\frac {1}{v}+{v^{\prime }}^{4}\right )^{{1}/{3}} \]

18458

\[ {} v^{\prime }+u^{2} v = \sin \left (u \right ) \]

18459

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

18460

\[ {} v^{\prime }+\frac {2 v}{u} = 3 \]

18461

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

18462

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

18463

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

18464

\[ {} x^{\prime } = k \left (A -n x\right ) \left (M -m x\right ) \]

18465

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

18466

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

18467

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

18468

\[ {} 2 a x +b y+\left (2 c y+b x +e \right ) y^{\prime } = g \]

18469

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

18470

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

18471

\[ {} \frac {2 x}{y^{3}}+\left (\frac {1}{y^{2}}-\frac {3 x^{2}}{y^{4}}\right ) y^{\prime } = 0 \]

18472

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

18473

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

18474

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

18475

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

18476

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

18477

\[ {} \left (T \ln \left (t \right )-1\right ) T = t T^{\prime } \]

18478

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

18479

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

18480

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

18481

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

18482

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

18483

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

18484

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

18485

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

18486

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

18487

\[ {} \sec \left (\theta \right )^{2} = \frac {m s^{\prime }}{k} \]

18488

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

18489

\[ {} \phi ^{\prime \prime } = \frac {4 \pi n c}{\sqrt {v_{0}^{2}+\frac {2 e \left (\phi -V_{0} \right )}{m}}} \]

18490

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

18491

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

18492

\[ {} v^{\prime }+\frac {2 v}{u} = 3 v \]

18493

\[ {} \sqrt {-u^{2}+1}\, v^{\prime } = 2 u \sqrt {1-v^{2}} \]

18494

\[ {} \sqrt {1+v^{\prime }} = \frac {{\mathrm e}^{u}}{2} \]

18495

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

18496

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

18497

\[ {} v^{\prime }+2 v u = 2 u \]

18498

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

18499

\[ {} u \ln \left (u \right ) v^{\prime }+\sin \left (v\right )^{2} = 1 \]

18500

\[ {} 4 y {y^{\prime }}^{3}-2 x^{2} {y^{\prime }}^{2}+4 x y y^{\prime }+x^{3} = 16 y^{2} \]