6.79 Problems 7801 to 7900

Table 6.157: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

7801

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

7802

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

7803

\[ {} y^{\prime }-5 y = 3 \,{\mathrm e}^{x}-2 x +1 \]

7804

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

7805

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

7806

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

7807

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

7808

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

7809

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

7810

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

7811

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

7812

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

7813

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

7814

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

7815

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

7816

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

7817

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

7818

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

7819

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

7820

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

7821

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

7822

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

7823

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

7824

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

7825

\[ {} y^{\prime \prime }-60 y^{\prime }-900 y = 5 \,{\mathrm e}^{10 x} \]

7826

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

7827

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

7828

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

7829

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

7830

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

7831

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

7832

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

7833

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

7834

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

7835

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

7836

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

7837

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

7838

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

7839

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

7840

\[ {} y^{\prime \prime }+5 y^{\prime }-3 y = \operatorname {Heaviside}\left (x -4\right ) \]

7841

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

7842

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

7843

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

7844

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

7845

\[ {} q^{\prime \prime }+9 q^{\prime }+14 q = \frac {\sin \left (t \right )}{2} \]

7846

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

7847

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

7848

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

7849

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

7850

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

7851

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

7852

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

7853

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

7854

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

7855

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

7856

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

7857

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

7858

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

7859

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

7860

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

7861

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

7862

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

7863

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

7864

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

7865

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

7866

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

7867

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

7868

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

7869

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

7870

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

7871

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

7872

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

7873

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

7874

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

7875

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

7876

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

7877

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

7878

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

7879

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

7880

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

7881

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

7882

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

7883

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

7884

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

7885

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

7886

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

7887

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

7888

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

7889

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

7890

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

7891

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

7892

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

7893

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

7894

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

7895

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

7896

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

7897

\[ {} 2 u^{2}+2 u v+\left (u^{2}+v^{2}\right ) v^{\prime } = 0 \]

7898

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

7899

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

7900

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