4.9.84 Problems 8301 to 8400

Table 4.1005: First order ode linear in derivative

#

ODE

Mathematica

Maple

Sympy

23329

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

23330

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

23331

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

23332

\[ {} y^{\prime } = \frac {3 x -2 y+7}{2 x +3 y+9} \]

23333

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

23334

\[ {} y^{\prime } = \frac {x -y+5}{2 x -y-3} \]

23335

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

23336

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

23337

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

23338

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

23339

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

23340

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

23341

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

23361

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

23364

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

23370

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

23372

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

23374

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

23385

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

23455

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

23746

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

23749

\[ {} y^{\prime }-3 y = 13 \cos \left (2 t \right ) \]

23763

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

23944

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

23945

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

23946

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

23947

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

23948

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

23949

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

23950

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

23951

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

23952

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

23953

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

23954

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

23955

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

23956

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

23957

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

23958

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

23959

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

23960

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

23961

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

23965

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

23966

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

23967

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

23968

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

23969

\[ {} y^{3}+y^{\prime } \sqrt {-x^{2}+1} = 0 \]

23970

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

23971

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

23972

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

23973

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

23974

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

23975

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

23976

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

23977

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

23978

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

23979

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

23980

\[ {} x \left (6 x^{2}+14 y^{2}\right )+y \left (13 x^{2}+30 y^{2}\right ) y^{\prime } = 0 \]

23981

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

23982

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

23983

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

23984

\[ {} y^{\prime } = \frac {x y+3}{5 x -y} \]

23985

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

23986

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

23987

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

23988

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

23989

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

23990

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

23991

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

23992

\[ {} y^{\prime } = 1+\frac {3 y}{x} \]

23993

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

23994

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

23995

\[ {} y^{\prime } = \frac {4 x -3 y-17}{3 x +y-3} \]

23996

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

23997

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

23998

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

23999

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

24000

\[ {} \frac {2 x}{y}+5 y^{2}-4 x +\left (3 y^{2}-\frac {x^{2}}{y^{2}}+10 x y\right ) y^{\prime } = 0 \]

24001

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

24002

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

24003

\[ {} \frac {1-6 x^{2} y}{x}+\frac {\left (2+5 y-3 x^{2} y\right ) y^{\prime }}{y} = 0 \]

24004

\[ {} \frac {8 x^{4} y+12 y^{2} x^{3}+2}{2 x +3 y}+\frac {\left (2 x^{5}+3 x^{4} y+3\right ) y^{\prime }}{x^{2} y^{4}+1} = 0 \]

24005

\[ {} \frac {y^{5} x^{2}+y^{2}+y}{x^{2} y^{4}+1}+\frac {\left (y^{4} x^{3}+2 x y+x \right ) y^{\prime }}{x^{2} y^{4}+1} = 0 \]

24006

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

24007

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

24008

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

24009

\[ {} 20 y-20 x y^{2}+\left (5 x -8 x^{2} y\right ) y^{\prime } = 0 \]

24010

\[ {} y^{3}+2 x y^{3}+1+3 x y^{2} y^{\prime } = 0 \]

24011

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

24012

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

24013

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

24014

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

24015

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

24016

\[ {} 2 x +2 x y^{2}-y^{3}-y^{5}+\left (1-3 x y^{2}-3 x y^{4}\right ) y^{\prime } = 0 \]

24017

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

24018

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

24019

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

24020

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

24021

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

24022

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

24023

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