2.49 Problems 4801 to 4900

Table 2.49: Main lookup table

#

ODE

Mathematica result

Maple result

4801

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

4802

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

4803

\[ {}x^{3} y^{\prime \prime }+4 x^{2} y^{\prime }+3 y = 0 \]

4804

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

4805

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

4806

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

4807

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

4808

\[ {}x^{2} \left (x -5\right )^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}-25\right ) y = 0 \]

4809

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

4810

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

4811

\[ {}x^{3} \left (x^{2}-25\right ) \left (-2+x \right )^{2} y^{\prime \prime }+3 x \left (-2+x \right ) y^{\prime }+7 \left (x +5\right ) y = 0 \]

4812

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

4813

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

4814

\[ {}x y^{\prime \prime }+\left (x +3\right ) y^{\prime }+7 x^{2} y = 0 \]

4815

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

4816

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

4817

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

4818

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

4819

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

4820

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

4821

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

4822

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

4823

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

4824

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

4825

\[ {}9 x^{2} y^{\prime \prime }+9 x^{2} y^{\prime }+2 y = 0 \]

4826

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

4827

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

4828

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

4829

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

4830

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

4831

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

4832

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

4833

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

4834

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

4835

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

4836

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

4837

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

4838

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

4839

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

4840

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

4841

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

4842

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

4843

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

4844

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

4845

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (36 x^{2}-\frac {1}{4}\right ) y = 0 \]

4846

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (25 x^{2}-\frac {4}{9}\right ) y = 0 \]

4847

\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (2 x^{2}-64\right ) y = 0 \]

4848

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

4849

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

4850

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

4851

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

4852

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

4853

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

4854

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

4855

\[ {}9 x^{2} y^{\prime \prime }+9 x y^{\prime }+\left (x^{6}-36\right ) y = 0 \]

4856

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

4857

\[ {}x y^{\prime \prime }+y^{\prime }-7 x^{3} y = 0 \]

4858

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

4859

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

4860

\[ {}16 x^{2} y^{\prime \prime }+32 x y^{\prime }+\left (x^{4}-12\right ) y = 0 \]

4861

\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (16 x^{4}+3\right ) y = 0 \]

4862

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

4863

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

4864

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

4865

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

4866

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

4867

\[ {}\cos \relax (x ) y^{\prime \prime }+y = 0 \]

4868

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

4869

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

4870

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

4871

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

4872

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

4873

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

4874

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

4875

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

4876

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

4877

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

4878

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

4879

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

4880

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

4881

\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+30 y = 0 \]

4882

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

4883

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

4884

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

4885

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

4886

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

4887

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

4888

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

4889

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

4890

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

4891

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

4892

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

4893

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

4894

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

4895

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

4896

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

4897

\[ {}4 x y^{\prime \prime }+y^{\prime }+8 y = 0 \]

4898

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

4899

\[ {}2 \left (t^{2}-5 t +6\right ) y^{\prime \prime }+\left (2 t -3\right ) y^{\prime }-8 y = 0 \]

4900

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