4.20.26 Problems 2501 to 2600

Table 4.1249: Second or higher order ODE with constant coefficients

#

ODE

Mathematica

Maple

Sympy

15367

\[ {} y^{\prime \prime \prime \prime }-16 y = 32 \operatorname {Heaviside}\left (t \right )-32 \operatorname {Heaviside}\left (t -\pi \right ) \]

15373

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

15374

\[ {} y^{\prime \prime }-2 y^{\prime }+5 y = {\mathrm e}^{t} \]

15375

\[ {} y^{\prime \prime }-3 y^{\prime }-7 y = 4 \]

15376

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

15377

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

15378

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

15413

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

15414

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

15416

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

15430

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

15431

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

15432

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

15435

\[ {} y^{\prime \prime }+9 y = 18 t \]

15436

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

15437

\[ {} y^{\prime \prime }-4 y^{\prime }+4 y = \left \{\begin {array}{cc} t & 0\le t \le 3 \\ t +2 & 3<t \end {array}\right . \]

15440

\[ {} c v^{\prime \prime }+\frac {v^{\prime }}{r}+\frac {v}{L} = \delta \left (t -1\right )-\delta \left (t \right ) \]

15446

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

15512

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

15515

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

15524

\[ {} y^{\prime \prime } = 9 y \]

15525

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

15526

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

15527

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

15528

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

15529

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

15530

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

15531

\[ {} 4 y^{\prime \prime }-12 y^{\prime }+9 y = 0 \]

15532

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

15533

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

15534

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

15535

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

15536

\[ {} y^{\left (5\right )}-4 y^{\prime \prime \prime } = 0 \]

15537

\[ {} y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+9 y = 0 \]

15538

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

15539

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

15540

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

15541

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

15542

\[ {} s^{\prime \prime }-a^{2} s = t +1 \]

15543

\[ {} y^{\prime \prime }+y^{\prime }-2 y = 8 \sin \left (2 x \right ) \]

15544

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

15545

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

15546

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

15547

\[ {} y^{\prime \prime }+9 y = 6 \,{\mathrm e}^{3 x} \]

15548

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

15549

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

15550

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

15551

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

15552

\[ {} y^{\prime \prime \prime \prime }-a^{4} y = 5 a^{4} {\mathrm e}^{a x} \sin \left (a x \right ) \]

15553

\[ {} a^{4} y+2 a^{2} y^{\prime \prime }+y^{\prime \prime \prime \prime } = 8 \cos \left (a x \right ) \]

15554

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

15555

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

15556

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

15557

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

15558

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

15565

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

15568

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

15600

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

15610

\[ {} y^{\prime \prime }-3 y^{\prime }-10 y = 0 \]

15611

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

15612

\[ {} y^{\prime \prime \prime }-7 y^{\prime \prime }+12 y^{\prime } = 0 \]

15622

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

15624

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

15627

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

15628

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

15629

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

15630

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

15767

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

15773

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

15774

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

15777

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

15778

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

15780

\[ {} y^{\prime \prime }-4 y = 31 \]

15781

\[ {} y^{\prime \prime }+9 y = 27 x +18 \]

15783

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

15784

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

15785

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

15786

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

15787

\[ {} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+8 y^{\prime \prime }-8 y^{\prime }+4 y = 0 \]

15788

\[ {} y^{\prime \prime \prime \prime }-8 y^{\prime } = 0 \]

15789

\[ {} 36 y^{\prime \prime \prime \prime }-12 y^{\prime \prime \prime }-11 y^{\prime \prime }+2 y^{\prime }+y = 0 \]

15790

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

15791

\[ {} y^{\left (5\right )}-y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }+35 y^{\prime \prime }+16 y^{\prime }-52 y = 0 \]

15792

\[ {} y^{\left (8\right )}+8 y^{\prime \prime \prime \prime }+16 y = 0 \]

15793

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

15794

\[ {} y^{\prime \prime \prime }+\left (-3-4 i\right ) y^{\prime \prime }+\left (-4+12 i\right ) y^{\prime }+12 y = 0 \]

15795

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

15797

\[ {} y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+13 y^{\prime \prime }-12 y^{\prime }+4 y = 2 \,{\mathrm e}^{x}-4 \,{\mathrm e}^{2 x} \]

15798

\[ {} y^{\prime \prime \prime \prime }+4 y^{\prime \prime } = 24 x^{2}-6 x +14+32 \cos \left (2 x \right ) \]

15799

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

15800

\[ {} y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime } = 6 x -20-120 x^{2} {\mathrm e}^{x} \]

15801

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+21 y^{\prime }-26 y = 36 \,{\mathrm e}^{2 x} \sin \left (3 x \right ) \]

15802

\[ {} y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y = \left (2 x^{2}+4 x +8\right ) \cos \left (x \right )+\left (6 x^{2}+8 x +12\right ) \sin \left (x \right ) \]

15803

\[ {} y^{\left (6\right )}-12 y^{\left (5\right )}+63 y^{\prime \prime \prime \prime }-18 y^{\prime \prime \prime }+315 y^{\prime \prime }-300 y^{\prime }+125 y = {\mathrm e}^{x} \left (48 \cos \left (x \right )+96 \sin \left (x \right )\right ) \]

15804

\[ {} y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+12 y = 0 \]

15805

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

15806

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

15807

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

15809

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

15811

\[ {} y^{\prime \prime }-9 y = 2 \sin \left (3 x \right ) \]