4.3.23 Problems 2201 to 2300

Table 4.409: Second order ode

#

ODE

Mathematica

Maple

Sympy

7382

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

7384

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

7386

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

7388

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

7390

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

7581

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

7582

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

7583

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

7584

\[ {} 2 y^{\prime \prime }+18 y = 0 \]

7585

\[ {} y^{\prime \prime }+6 y^{\prime }+12 y = 0 \]

7586

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

7587

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

7588

\[ {} y^{\prime \prime }+2 y^{\prime }+5 y = -50 \sin \left (5 t \right ) \]

7589

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

7590

\[ {} m y^{\prime \prime }+b y^{\prime }+k y = \cos \left (\omega t \right ) \]

7591

\[ {} y^{\prime \prime }+\frac {y^{\prime }}{10}+25 y = \cos \left (\omega t \right ) \]

7592

\[ {} y^{\prime \prime }+25 y = \cos \left (\omega t \right ) \]

7593

\[ {} 2 y^{\prime \prime }+7 y^{\prime }-4 y = 0 \]

7594

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

7595

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

7596

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

7597

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

7598

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

7599

\[ {} 6 y^{\prime \prime }+y^{\prime }-2 y = 0 \]

7600

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

7601

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

7602

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

7603

\[ {} 4 w^{\prime \prime }+20 w^{\prime }+25 w = 0 \]

7604

\[ {} 3 y^{\prime \prime }+11 y^{\prime }-7 y = 0 \]

7605

\[ {} y^{\prime \prime }+2 y^{\prime }-8 y = 0 \]

7606

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

7607

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

7608

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

7609

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

7610

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

7611

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

7612

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

7617

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

7618

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

7619

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

7630

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

7631

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

7632

\[ {} y^{\prime \prime }+\operatorname {dif} \left (y, t\right )-6 y = 0 \]

7676

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

7678

\[ {} x^{\prime \prime }+42 x^{\prime }+x = 0 \]

7681

\[ {} x^{\prime \prime }+2 \gamma x^{\prime }+\omega _{0} x = F \cos \left (\omega t \right ) \]

7682

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

7683

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

7684

\[ {} y^{\prime \prime }+16 y = 16 \cos \left (4 x \right ) \]

7685

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

7695

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

7696

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

7697

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

7698

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

7699

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

7700

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

7701

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

7702

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

7705

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

7766

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

7767

\[ {} y^{\prime \prime }-4 y = 10 \,{\mathrm e}^{3 x} \]

7768

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

7769

\[ {} y^{\prime \prime }+25 y = 5 x^{2}+x \]

7770

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

7771

\[ {} 5 y+4 y^{\prime }+y^{\prime \prime } = 2 \,{\mathrm e}^{-2 x} \]

7772

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

7773

\[ {} y^{\prime \prime }-6 y^{\prime }+8 y = 8 \,{\mathrm e}^{4 x} \]

7774

\[ {} 2 y^{\prime \prime }-7 y^{\prime }-4 y = {\mathrm e}^{3 x} \]

7775

\[ {} y^{\prime \prime }-6 y^{\prime }+9 y = 54 x +18 \]

7776

\[ {} y^{\prime \prime }-5 y^{\prime }+6 y = 100 \sin \left (4 x \right ) \]

7777

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

7778

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

7779

\[ {} y^{\prime \prime }-y^{\prime }+10 y = 20-{\mathrm e}^{2 x} \]

7780

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

7781

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

7782

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

7783

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

7784

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

7785

\[ {} y^{\prime \prime }+4 y^{\prime }+5 y = 6 \sin \left (t \right ) \]

7786

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

7787

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

7788

\[ {} y^{\prime \prime }+6 y^{\prime }+10 y = 50 x \]

7789

\[ {} x^{\prime \prime }+2 x^{\prime }+2 x = 85 \sin \left (3 t \right ) \]

7790

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

7791

\[ {} \frac {x^{\prime \prime }}{2} = -48 x \]

7792

\[ {} x^{\prime \prime }+5 x^{\prime }+6 x = \cos \left (t \right ) \]

7793

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

7794

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

7795

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

7796

\[ {} y^{\prime \prime }-6 y^{\prime }+25 y = 2 \sin \left (\frac {t}{2}\right )-\cos \left (\frac {t}{2}\right ) \]

7797

\[ {} y^{\prime \prime }-6 y^{\prime }+25 y = 64 \,{\mathrm e}^{-t} \]

7798

\[ {} y^{\prime \prime }-6 y^{\prime }+25 y = 50 t^{3}-36 t^{2}-63 t +18 \]

7800

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

7801

\[ {} y^{\prime \prime }-5 y = 2 \,{\mathrm e}^{5 x} \]

7805

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

7806

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

7807

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

7808

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

7809

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

7816

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