3.24.11 Problems 1001 to 1100

Table 3.827: Second or higher order ODE with non-constant coefficients

#

ODE

Mathematica

Maple

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

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

7778

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

7779

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

7780

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

7781

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

7782

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

7783

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

7784

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

7785

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

7786

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

7787

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

7788

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

7789

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

7790

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

7791

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

7792

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

7793

\[ {}x^{2} \left (1-x \right ) y^{\prime \prime }+\left (5 x -4\right ) x y^{\prime }+\left (6-9 x \right ) y = 0 \]

7794

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

7795

\[ {}y^{\prime \prime }-2 x y^{\prime }+8 y = 0 \]

7796

\[ {}y^{\prime \prime }-2 x y^{\prime }+8 y = 0 \]

7797

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

7798

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

7799

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

7800

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

7801

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

7802

\[ {}\left (x^{2}-2 x +10\right ) y^{\prime \prime }+x y^{\prime }-4 y = 0 \]

7803

\[ {}\left (x^{2}-2 x +10\right ) y^{\prime \prime }+x y^{\prime }-4 y = 0 \]

7804

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

7805

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

7806

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

7807

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

7808

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

7809

\[ {}y^{\prime \prime }-2 x y^{\prime }+8 y = 0 \]

7810

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

7811

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

7812

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

7813

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

7814

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

7815

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

7816

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

7817

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

7818

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