5.4.7 Problems 601 to 700

Table 5.427: Second ODE homogeneous ODE

#

ODE

Mathematica

Maple

6701

\[ {}y^{\prime \prime }+2 y^{\prime }-15 y = 0 \]

6703

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

6705

\[ {}y^{\prime \prime }-4 y^{\prime }+13 y = 0 \]

6706

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

6755

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

6759

\[ {}y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }-10 y = 0 \]

6761

\[ {}4 x^{2} y^{\prime \prime }+4 x^{3} y^{\prime }+\left (x^{2}+1\right )^{2} y = 0 \]

6763

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

6769

\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (9 x^{2}+6\right ) y = 0 \]

6776

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

6777

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

6778

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

6781

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

6786

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

6879

\[ {}u^{\prime \prime }+u^{\prime }+u = \cos \left (r +u\right ) \]

6880

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

6881

\[ {}R^{\prime \prime } = -\frac {k}{R^{2}} \]

6882

\[ {}x^{\prime \prime }-\left (1-\frac {{x^{\prime }}^{2}}{3}\right ) x^{\prime }+x = 0 \]

6888

\[ {}y^{\prime \prime }-6 y^{\prime }+13 y = 0 \]

6898

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

6908

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

6909

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

6910

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

6911

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

6912

\[ {}x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y = 0 \]

6939

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

6940

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

6941

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

6942

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

6943

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

6944

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

6945

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

6946

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

6971

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

6972

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

6973

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

6974

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

6975

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

6976

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

6979

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

6987

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

6988

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

6998

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

7002

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

7006

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

7349

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

7351

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

7354

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

7358

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

7362

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

7478

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

7479

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

7480

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

7481

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

7482

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

7483

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

7484

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

7486

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

7487

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

7489

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

7517

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

7518

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

7519

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

7523

\[ {}y^{\prime \prime }+2 x^{2} y^{\prime }+\left (x^{4}+2 x -1\right ) y = 0 \]

7525

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

7527

\[ {}y^{\prime \prime }-\frac {x y^{\prime }}{-x^{2}+1}+\frac {y}{-x^{2}+1} = 0 \]

7528

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

7533

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

7535

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

7542

\[ {}y^{\prime \prime }+2 y^{\prime }+\left (1+\frac {2}{\left (1+3 x \right )^{2}}\right ) y = 0 \]

7545

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

7546

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

7551

\[ {}u^{\prime \prime }-\cot \left (\theta \right ) u^{\prime } = 0 \]

7557

\[ {}y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {y \left (-8+\sqrt {x}+x \right )}{4 x^{2}} = 0 \]

7558

\[ {}\left (-x^{2}+1\right ) z^{\prime \prime }+\left (1-3 x \right ) z^{\prime }+k z = 0 \]

7559

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

7565

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

7585

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

7586

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

7587

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

7612

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

7613

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

7614

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

7615

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

7616

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

7617

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

7618

\[ {}y^{\prime \prime }+\left (-1+3 i\right ) y^{\prime }-3 i y = 0 \]

7619

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

7620

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

7621

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

7622

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

7623

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

7624

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

7625

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

7626

\[ {}y^{\prime \prime }+\left (1+4 i\right ) y^{\prime }+y = 0 \]

7627

\[ {}y^{\prime \prime }+\left (-1+3 i\right ) y^{\prime }-3 i y = 0 \]

7628

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

7650

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

7651

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

7657

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