3.3.20 Problems 1901 to 2000

Table 3.271: Second order ode

#

ODE

Mathematica

Maple

7678

\[ {}4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+8 x y^{\prime }-\left (-x^{2}+35\right ) y = 0 \]

7679

\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-x^{2}+5\right ) y^{\prime }-\left (25 x^{2}+7\right ) y = 0 \]

7680

\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (2 x^{2}+5\right ) y^{\prime }-21 y = 0 \]

7681

\[ {}4 x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+4 x \left (x^{2}+2\right ) y^{\prime }-\left (x^{2}+15\right ) y = 0 \]

7682

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

7683

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

7684

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

7685

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

7686

\[ {}\left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+6 y = 0 \]

7687

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

7688

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

7689

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

7690

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

7691

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

7692

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

7693

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

7694

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

7695

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

7696

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

7697

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

7698

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

7699

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

7700

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

7701

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

7702

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

7703

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

7704

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

7705

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

7706

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

7707

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

7708

\[ {}z y^{\prime \prime }+\left (2 z -3\right ) y^{\prime }+\frac {4 y}{z} = 0 \]

7709

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

7710

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

7711

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

7712

\[ {}\left (-4 x^{2}+1\right ) y^{\prime \prime }-20 x y^{\prime }-16 y = 0 \]

7713

\[ {}\left (x^{2}-1\right ) y^{\prime \prime }-6 x y^{\prime }+12 y = 0 \]

7714

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

7715

\[ {}\left (2 x^{2}+1\right ) y^{\prime \prime }+7 x y^{\prime }+2 y = 0 \]

7716

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

7717

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

7718

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

7719

\[ {}6 x^{2} y^{\prime \prime }+x \left (1+18 x \right ) y^{\prime }+\left (1+12 x \right ) y = 0 \]

7720

\[ {}3 x^{2} y^{\prime \prime }-x \left (8+x \right ) y^{\prime }+6 y = 0 \]

7721

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

7722

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

7723

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

7724

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

7725

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

7726

\[ {}x^{2} y^{\prime \prime }-\left (2 \sqrt {5}-1\right ) x y^{\prime }+\left (\frac {19}{4}-3 x^{2}\right ) y = 0 \]

7727

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

7728

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

7729

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

7730

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

7731

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

7732

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

7733

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

7734

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

7735

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

7736

\[ {}x^{2} y^{\prime \prime }+x \left (5-x \right ) y^{\prime }+4 y = 0 \]

7737

\[ {}4 x^{2} y^{\prime \prime }+4 x \left (1-x \right ) y^{\prime }+\left (2 x -9\right ) y = 0 \]

7738

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

7739

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

7740

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

7741

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

7742

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

7743

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

7744

\[ {}2 x y^{\prime \prime }+5 \left (-2 x +1\right ) y^{\prime }-5 y = 0 \]

7745

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

7746

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

7747

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

7748

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

7749

\[ {}\left (4 x^{3}-14 x^{2}-2 x \right ) y^{\prime \prime }-\left (6 x^{2}-7 x +1\right ) y^{\prime }+\left (6 x -1\right ) y = 0 \]

7750

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

7751

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

7752

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

7753

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

7754

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

7755

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

7756

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

7757

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

7758

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

7759

\[ {}2 x \left (1-x \right ) y^{\prime \prime }+\left (1-11 x \right ) y^{\prime }-10 y = 0 \]

7760

\[ {}x \left (1-x \right ) y^{\prime \prime }+\frac {\left (-2 x +1\right ) y^{\prime }}{3}+\frac {20 y}{9} = 0 \]

7761

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

7762

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

7763

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

7764

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

7765

\[ {}u^{\prime \prime }+\frac {4 u^{\prime }}{x}-a^{2} u = 0 \]

7766

\[ {}u^{\prime \prime }+\frac {4 u^{\prime }}{x}+a^{2} u = 0 \]

7767

\[ {}y^{\prime \prime }-a^{2} y = \frac {6 y}{x^{2}} \]

7768

\[ {}y^{\prime \prime }+n^{2} y = \frac {6 y}{x^{2}} \]

7769

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

7770

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

7771

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {25}{4}\right ) y = 0 \]

7772

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

7773

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

7774

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

7775

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

7776

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

7777

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