4.3.55 Problems 5401 to 5500

Table 4.473: Second order ode

#

ODE

Mathematica

Maple

Sympy

15430

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

15431

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

15432

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

15433

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

15434

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

15435

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

15436

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

15437

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

15439

\[ {} x^{\prime \prime }+2 t x^{\prime }-4 x = 1 \]

15440

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

15446

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

15447

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

15448

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

15513

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

15515

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

15516

\[ {} y^{\prime \prime } = \frac {a}{y^{3}} \]

15517

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

15518

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

15519

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

15520

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

15521

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

15524

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

15525

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

15526

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

15527

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

15528

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

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

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

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

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

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

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

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

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

15562

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

15565

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

15568

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

15591

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

15592

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

15593

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

15594

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

15595

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

15597

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

15599

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

15600

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

15601

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

15607

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

15610

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

15611

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

15614

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

15615

\[ {} x^{2} y^{\prime \prime }+6 x y^{\prime }+4 y = 0 \]

15616

\[ {} x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 0 \]

15622

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

15624

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

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

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

15632

\[ {} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \]

15633

\[ {} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \]

15634

\[ {} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \]

15635

\[ {} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \]

15636

\[ {} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \]

15637

\[ {} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \]

15767

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

15769

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

15770

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

15771

\[ {} \sqrt {1-x}\, y^{\prime \prime }-4 y = \sin \left (x \right ) \]

15772

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

15773

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

15774

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

15775

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

15776

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

15777

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

15779

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

15780

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

15781

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

15782

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

15783

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

15793

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

15809

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

15811

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

15812

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

15813

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

15817

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

15818

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

15819

\[ {} y^{\prime \prime }-y^{\prime }+6 y = -2 \sin \left (3 x \right ) \]

15820

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

15824

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