6.209 Problems 20801 to 20900

Table 6.417: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

20801

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

20802

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

20803

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

20804

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

20805

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

20806

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

20807

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

20808

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

20809

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

20810

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

20811

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

20812

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

20813

\[ {} 2 y^{\prime \prime }+9 y^{\prime }-18 y = 0 \]

20814

\[ {} y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-9 y^{\prime \prime }-11 y^{\prime }-4 y = 0 \]

20815

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

20816

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

20817

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

20818

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

20819

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

20820

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

20821

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

20822

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

20823

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

20824

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

20825

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

20826

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

20827

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

20828

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

20829

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

20830

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

20831

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

20832

\[ {} y-\frac {1}{\sqrt {1+{y^{\prime }}^{2}}} = b \]

20833

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

20834

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

20835

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

20836

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

20837

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

20838

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

20839

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

20840

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

20841

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

20842

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

20843

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

20844

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

20845

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

20846

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

20847

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

20848

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

20849

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

20850

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

20851

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

20852

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

20853

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

20854

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

20855

\[ {} {y^{\prime }}^{3}-4 y y^{\prime } x +8 y^{2} = 0 \]

20856

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

20857

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

20858

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

20859

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

20860

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

20861

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

20862

\[ {} x y-x^{2} y^{\prime }+2 x^{3} y^{\prime \prime }+x^{4} y^{\prime \prime \prime } = 1 \]

20863

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

20864

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

20865

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

20866

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

20867

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

20868

\[ {} 2 y+2 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime } = 10 x +\frac {10}{x} \]

20869

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

20870

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

20871

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

20872

\[ {} 16 \left (1+x \right )^{4} y^{\prime \prime \prime \prime }+96 \left (1+x \right )^{3} y^{\prime \prime \prime }+104 \left (1+x \right )^{2} y^{\prime \prime }+8 y^{\prime } \left (1+x \right )+y = x^{2}+4 x +3 \]

20873

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

20874

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

20875

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

20876

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

20877

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

20878

\[ {} \left (x^{3}-x \right ) y^{\prime \prime \prime }+\left (8 x^{2}-3\right ) y^{\prime \prime }+14 x y^{\prime }+4 y = \frac {2}{x^{3}} \]

20879

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

20880

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

20881

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

20882

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

20883

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

20884

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

20885

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

20886

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

20887

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

20888

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

20889

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

20890

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

20891

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

20892

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

20893

\[ {} y^{\prime }-y y^{\prime \prime } = n \sqrt {{y^{\prime }}^{2}+a^{2} y^{\prime \prime }} \]

20894

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

20895

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

20896

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

20897

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

20898

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

20899

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

20900

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