5.20.37 Problems 3601 to 3700

Table 5.979: Second or higher order ODE with constant coefficients

#

ODE

Mathematica

Maple

18391

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

18392

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

18393

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

18394

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

18395

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

18396

\[ {}y^{\prime \prime }-7 y^{\prime }+12 y = {\mathrm e}^{2 x} \left (x^{3}-5 x^{2}\right ) \]

18397

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

18398

\[ {}y^{\prime \prime \prime }-8 y = 16 x^{2} \]

18399

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

18400

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

18401

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

18402

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

18403

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

18404

\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y = {\mathrm e}^{2 x} \]

18405

\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y = 12 \,{\mathrm e}^{-x} \]

18406

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

18453

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

18454

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

18455

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

18456

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

18457

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

18461

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

18462

\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = 4 \,{\mathrm e}^{3 t} \]

18463

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

18464

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

18465

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

18517

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

18518

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

18519

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

18520

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

18521

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

18522

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

18523

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

18524

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

18525

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

18526

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

18527

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

18528

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

18529

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

18530

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

18565

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

18580

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

18581

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

18582

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

18583

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

18584

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

18585

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

18586

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

18587

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

18589

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

18592

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

18593

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

18594

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

18599

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

18607

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

18655

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

18656

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

18657

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

18658

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

18659

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

18660

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

18661

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

18662

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

18663

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

18664

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

18665

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

18666

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

18667

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

18668

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

18669

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

18670

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

18671

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

18672

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

18673

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

18674

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

18675

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

18676

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

18677

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

18678

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

18679

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

18680

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

18681

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

18682

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

18683

\[ {}e y^{\prime \prime } = P \left (-y+a \right ) \]

18698

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

18700

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

18706

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

18726

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

18867

\[ {}y^{\prime \prime }+3 y^{\prime }-54 y = 0 \]

18868

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

18869

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

18870

\[ {}9 y^{\prime \prime }+18 y^{\prime }-16 y = 0 \]

18871

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

18872

\[ {}y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-9 y^{\prime \prime }-11 y^{\prime }-4 y = 0 \]

18873

\[ {}y^{\prime \prime }+8 y^{\prime }+25 y = 0 \]

18874

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

18875

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

18876

\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = {\mathrm e}^{4 x} \]

18877

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

18878

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