5.3.17 Problems 1601 to 1700

Table 5.317: Second order ode

#

ODE

Mathematica

Maple

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

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

7629

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

7630

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

7631

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

7632

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

7633

\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = 3 \,{\mathrm e}^{-x}+2 x^{2} \]

7634

\[ {}y^{\prime \prime }-7 y^{\prime }+6 y = \sin \left (x \right ) \]

7635

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

7636

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

7637

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

7638

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

7639

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

7650

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

7651

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

7657

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

7664

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

7665

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

7666

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

7667

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

7668

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

7669

\[ {}y^{\prime \prime }+9 y = x^{2} {\mathrm e}^{3 x} \]

7670

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

7671

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

7674

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

7675

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

7676

\[ {}\left (3 x -1\right )^{2} y^{\prime \prime }+\left (9 x -3\right ) y^{\prime }-9 y = 0 \]

7677

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

7678

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

7679

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

7680

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

7681

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

7682

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

7684

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

7685

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

7686

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

7697

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

7698

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

7699

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

7700

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

7701

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

7702

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

7704

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

7705

\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+5 y = 0 \]

7706

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

7707

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

7759

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

7760

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

7761

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

7762

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

7763

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

7764

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

7765

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

7766

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

7767

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

7768

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

7777

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

7778

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

7804

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

7823

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

7824

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

7905

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

7906

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

7907

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

7908

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

7909

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

7910

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

7911

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

7912

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

7913

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

7914

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

7915

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

7916

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

7933

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

7934

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

7935

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

7936

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

7937

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

7938

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

7939

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

7940

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

7941

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

7942

\[ {}y^{\prime \prime }-9 y^{\prime }+20 y = 0 \]

7943

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

7944

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

7945

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

7946

\[ {}y^{\prime \prime }-6 y^{\prime }+25 y = 0 \]

7947

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

7948

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

7949

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