6.249 Problems 24801 to 24900

Table 6.497: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

24801

\[ {} 2 y-3 y^{\prime }+y^{\prime \prime } = 6 x^{2}-6 x -11 \]

24802

\[ {} 2 y-3 y^{\prime }+y^{\prime \prime } = 2 x^{3}-9 x^{2}+2 x -16 \]

24803

\[ {} y^{\left (6\right )}-y = x^{10} \]

24804

\[ {} y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y = 16 x^{3}+20 x^{2} \]

24805

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

24806

\[ {} y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{3 x} \]

24807

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

24808

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

24809

\[ {} 4 y+y^{\prime \prime } = 8 x^{5} \]

24810

\[ {} 4 y+y^{\prime \prime } = 16 x \,{\mathrm e}^{2 x} \]

24811

\[ {} 5 y+4 y^{\prime }+y^{\prime \prime } = 4 \,{\mathrm e}^{-2 x} \cos \left (x \right ) \]

24812

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

24813

\[ {} y^{\prime \prime }-4 y^{\prime }+13 y = 24 \,{\mathrm e}^{2 x} \sin \left (3 x \right ) \]

24814

\[ {} y^{\prime \prime }-4 y^{\prime }+13 y = 24 \,{\mathrm e}^{2 x} \sin \left (x \right ) \]

24815

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

24816

\[ {} 2 y-3 y^{\prime }+y^{\prime \prime } = 72 x \,{\mathrm e}^{-x} \]

24817

\[ {} 4 y+y^{\prime \prime } = 12 \sin \left (x \right )+12 \sin \left (2 x \right ) \]

24818

\[ {} 4 y+y^{\prime \prime } = 20 \,{\mathrm e}^{x}-20 \cos \left (2 x \right ) \]

24819

\[ {} y^{\prime \prime }+16 y = 8 x +8 \sin \left (4 x \right ) \]

24820

\[ {} 4 y+y^{\prime \prime } = 8 \cos \left (x \right ) \sin \left (x \right ) \]

24821

\[ {} 4 y+y^{\prime \prime } = 8 \cos \left (x \right )^{2} \]

24822

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

24823

\[ {} y^{\prime \prime }-4 y^{\prime }+13 y = 24 \,{\mathrm e}^{2 x} \cos \left (x \right ) \]

24824

\[ {} y^{\prime \prime }-4 y^{\prime }+13 y = 24 \,{\mathrm e}^{2 x} \cos \left (3 x \right ) \]

24825

\[ {} y^{\prime \prime }+25 y = \sin \left (5 x \right ) \]

24826

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

24827

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

24828

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

24829

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

24830

\[ {} 4 y+y^{\prime \prime } = -8+2 x \]

24831

\[ {} y^{\prime \prime }+3 y^{\prime }+2 y = 4 x^{2} \]

24832

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

24833

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

24834

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

24835

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

24836

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

24837

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

24838

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

24839

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

24840

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

24841

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

24842

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

24843

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

24844

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

24845

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

24846

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

24847

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

24848

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

24849

\[ {} 2 y-3 y^{\prime }+y^{\prime \prime } = \frac {{\mathrm e}^{2 x}}{{\mathrm e}^{2 x}+1} \]

24850

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

24851

\[ {} -y+y^{\prime \prime } = \frac {2}{\sqrt {1-{\mathrm e}^{-2 x}}} \]

24852

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

24853

\[ {} y^{\prime \prime }-5 y^{\prime }+4 y = \frac {6}{1+{\mathrm e}^{-2 x}} \]

24854

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

24855

\[ {} y^{\prime \prime }-4 y^{\prime }-3 y = \cos \left ({\mathrm e}^{-x}\right ) \]

24856

\[ {} 2 y-3 y^{\prime }+y^{\prime \prime } = 15 \sqrt {1+{\mathrm e}^{-x}} \]

24857

\[ {} 2 y-3 y^{\prime }+y^{\prime \prime } = \frac {1}{\sqrt {1+{\mathrm e}^{-2 x}}} \]

24858

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

24859

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

24860

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

24861

\[ {} y^{\prime \prime }-4 y^{\prime }+3 y = \sin \left ({\mathrm e}^{-x}\right ) \]

24862

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

24863

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

24864

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

24865

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

24866

\[ {} 2 y-3 y^{\prime }+y^{\prime \prime } = \frac {1}{\sqrt {1+{\mathrm e}^{-2 x}}} \]

24867

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

24868

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

24869

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

24870

\[ {} -y+y^{\prime \prime } = {\mathrm e}^{2 x} \left (3 \tan \left ({\mathrm e}^{x}\right )+{\mathrm e}^{x} \sec \left ({\mathrm e}^{x}\right )^{2}\right ) \]

24871

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

24872

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

24873

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

24874

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

24875

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

24876

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

24877

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

24878

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

24879

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

24880

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

24881

\[ {} y^{\prime \prime }+4 y^{\prime }+3 y = \sin \left ({\mathrm e}^{x}\right ) \]

24882

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

24883

\[ {} [v^{\prime }\left (x \right )-2 v \left (x \right )+2 w^{\prime }\left (x \right ) = 2-4 \,{\mathrm e}^{2 x}, 2 v^{\prime }\left (x \right )-3 v \left (x \right )+3 w^{\prime }\left (x \right )-w \left (x \right ) = 0] \]

24884

\[ {} [y^{\prime }\left (x \right )-2 y \left (x \right )-v^{\prime }\left (x \right )-v \left (x \right ) = 6 \,{\mathrm e}^{3 x}, 2 y^{\prime }\left (x \right )-3 y \left (x \right )+v^{\prime }\left (x \right )-3 v \left (x \right ) = 6 \,{\mathrm e}^{3 x}] \]

24885

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

24886

\[ {} [2 v^{\prime }\left (x \right )+2 v \left (x \right )+w^{\prime }\left (x \right )-w \left (x \right ) = 3 x, v^{\prime }\left (x \right )+v \left (x \right )+w^{\prime }\left (x \right )+w \left (x \right ) = 1] \]

24887

\[ {} [3 v^{\prime }\left (x \right )+2 v \left (x \right )+w^{\prime }\left (x \right )-6 w \left (x \right ) = 5 \,{\mathrm e}^{x}, 4 v^{\prime }\left (x \right )+2 v \left (x \right )+w^{\prime }\left (x \right )-8 w \left (x \right ) = 5 \,{\mathrm e}^{x}+2 x -3] \]

24888

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

24889

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

24890

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

24891

\[ {} x^{2} {y^{\prime }}^{2}-7 y y^{\prime } x +12 y^{2} = 0 \]

24892

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

24893

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

24894

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

24895

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

24896

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

24897

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

24898

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

24899

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

24900

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