4.1.86 Problems 8501 to 8600

Table 4.171: First order ode

#

ODE

Mathematica

Maple

Sympy

20795

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

20796

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

20797

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

20798

\[ {} 1+y^{2}-y y^{\prime } x = 0 \]

20799

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

20800

\[ {} y^{\prime } = \frac {6 x -2 y-7}{2 x +3 y-6} \]

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

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

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

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

20927

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

20928

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

20929

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

20930

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

20931

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

20932

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

20933

\[ {} s^{\prime }+2 s = s t^{2} \]

20934

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

20935

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

20936

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

20937

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

20938

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

20939

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

20940

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

20941

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

20942

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

20943

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

20944

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

20945

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

20946

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

20947

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

20948

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

20949

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

20950

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

20951

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

20952

\[ {} x^{2}+2 x y-4 y^{2}-\left (x^{2}-8 x y-4 y^{2}\right ) y^{\prime } = 0 \]

21064

\[ {} y^{\prime } = k y-c y^{2} \]

21065

\[ {} y^{\prime } = y^{2}-6 y-16 \]

21066

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

21067

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

21068

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

21069

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

21070

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

21071

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

21072

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

21073

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

21074

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

21075

\[ {} x^{\prime } = \mu -x^{3} \]

21076

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

21077

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

21078

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

21079

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

21080

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

21081

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

21082

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

21083

\[ {} y^{\prime } = 3 y^{{2}/{3}} \]

21084

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

21085

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