3.4.28 Problems 2701 to 2800

Table 3.391: Second ODE homogeneous ODE

#

ODE

Mathematica

Maple

12413

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

12414

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

12415

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

12416

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

12424

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

12425

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

12490

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

12492

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

12493

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

12495

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

12498

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

12501

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

12502

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

12503

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

12504

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

12505

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

12506

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

12507

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

12508

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

12509

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

12531

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

12568

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

12569

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

12570

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

12571

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

12572

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

12574

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

12576

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

12577

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

12578

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

12584

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

12587

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

12588

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

12591

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

12592

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

12593

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

12599

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

12601

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

12604

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

12605

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

12606

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

12607

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

12609

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

12610

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

12611

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

12612

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

12613

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

12614

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

12750

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

12751

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

12752

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

12753

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

12754

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

12756

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

12760

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

12770

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

12786

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

12803

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

13126

\[ {}y^{\prime \prime }-6 y^{\prime }-7 y = 0 \]

13127

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

13157

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

13158

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

13159

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

13160

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

13239

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

13241

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

13252

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

13474

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

13475

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

13477

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

13478

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

13479

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

13481

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

13482

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

13484

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

13486

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

13492

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

13493

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

13494

\[ {}\sin \left (y\right ) y^{\prime \prime }+\cos \left (y\right ) {y^{\prime }}^{2} = 0 \]

13495

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

13496

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

13497

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

13498

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

13500

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

13502

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

13503

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

13504

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

13506

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

13508

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

13509

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

13515

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

13516

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

13517

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

13518

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

13519

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

13520

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

13521

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

13522

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

13523

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

13524

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