4.20.43 Problems 4201 to 4300

Table 4.1283: Second or higher order ODE with constant coefficients

#

ODE

Mathematica

Maple

Sympy

21415

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

21416

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

21422

\[ {} x^{\prime \prime \prime }+a x^{\prime \prime }+b x^{\prime }+c x = 0 \]

21424

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

21425

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

21426

\[ {} x^{\prime \prime \prime }+5 x^{\prime \prime }+9 x^{\prime }+5 x = 0 \]

21427

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

21428

\[ {} x^{\prime \prime \prime \prime }+8 x^{\prime \prime \prime }+23 x^{\prime \prime }+2 x^{\prime }+12 x = 0 \]

21591

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

21592

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

21593

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

21594

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

21595

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

21596

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

21597

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

21598

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

21599

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

21600

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

21601

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

21602

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

21603

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

21604

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

21605

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

21606

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

21607

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

21608

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

21609

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

21610

\[ {} y^{\prime \prime }-6 y^{\prime }+9 y = 0 \]

21611

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

21612

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

21613

\[ {} y^{\prime \prime }+16 y = 0 \]

21614

\[ {} y^{\prime \prime }-6 y^{\prime }+25 y = 0 \]

21615

\[ {} y^{\prime \prime }-\frac {6 y^{\prime }}{5}+\frac {9 y}{25} = 0 \]

21616

\[ {} y^{\prime \prime \prime }-4 y^{\prime \prime }+y^{\prime }+6 y = 0 \]

21617

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

21618

\[ {} y^{\prime \prime \prime }-4 y^{\prime \prime }+y^{\prime }+6 y = 0 \]

21619

\[ {} y^{\prime \prime \prime }-4 y^{\prime \prime }-3 y^{\prime }+18 y = 0 \]

21620

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = 0 \]

21621

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

21622

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

21623

\[ {} y^{\prime \prime \prime \prime }-7 y^{\prime \prime \prime }+18 y^{\prime \prime }-20 y^{\prime }+8 y = 0 \]

21624

\[ {} y^{\prime \prime \prime \prime }+8 y^{\prime \prime \prime }+24 y^{\prime \prime }+32 y^{\prime }+16 y = 0 \]

21630

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

21631

\[ {} y^{\prime \prime } = 9 x^{2}+2 x -1 \]

21632

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

21633

\[ {} y^{\prime \prime }+5 y^{\prime }+6 y = x^{2}+2 x \]

21634

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

21635

\[ {} y^{\prime \prime }+y^{\prime }-6 y = 2 x^{3}+5 x^{2}-7 x +2 \]

21636

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

21637

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

21638

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

21639

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

21640

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

21641

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

21642

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

21643

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

21644

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

21645

\[ {} y^{\prime \prime }+y^{\prime }+8 y = \left (10 x^{2}+21 x +9\right ) \sin \left (3 x \right )+x \cos \left (3 x \right ) \]

21646

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

21647

\[ {} y^{\prime \prime }+y^{\prime }-2 y = 2 x -40 \cos \left (2 x \right ) \]

21648

\[ {} y^{\prime \prime }-2 y^{\prime }-3 y = 2 \,{\mathrm e}^{x}-10 \sin \left (x \right ) \]

21649

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

21650

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

21651

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = 2 x \,{\mathrm e}^{-x} \]

21652

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

21653

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

21655

\[ {} y^{\prime \prime }+5 y^{\prime }+6 y = x^{2}+2 x \]

21656

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

21657

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

21658

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

21659

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

21660

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

21661

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

21662

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

21663

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

21664

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

21666

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

21667

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

21668

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

21679

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

21682

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

21683

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

21684

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

21685

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

21686

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

21687

\[ {} 2 y^{\prime \prime }+5 y^{\prime }-12 y = 0 \]

21688

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

21689

\[ {} y^{\prime \prime \prime \prime }+12 y^{\prime \prime \prime }+54 y^{\prime \prime }+108 y^{\prime }+81 y = 0 \]

21690

\[ {} y^{\left (6\right )}+8 y^{\prime \prime \prime } = a \,{\mathrm e}^{x} \]

21691

\[ {} y^{\prime \prime }-2 y^{\prime }+5 y = 16 x^{3} {\mathrm e}^{3 x} \]

21692

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

21693

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

21694

\[ {} y^{\prime \prime \prime \prime }+8 y^{\prime \prime \prime }+16 y^{\prime \prime } = 96 \,{\mathrm e}^{-4 x} \]

21695

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

21696

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

21697

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

21698

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

21699

\[ {} y^{\prime \prime \prime }-5 y^{\prime \prime }+3 y^{\prime }+9 y = {\mathrm e}^{3 x} \]

21700

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

21701

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