4.9.71 Problems 7001 to 7100

Table 4.765: First order ode linear in derivative

#

ODE

Mathematica

Maple

Sympy

18679

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

18680

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

18681

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

18682

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

18683

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

18684

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

18685

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

18686

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

18687

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

18688

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

18689

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

18690

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

18691

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

18692

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

18693

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

18694

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

18695

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

18696

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

18697

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

18698

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

18699

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

18700

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

18701

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

18702

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

18703

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

18704

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

18705

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

18706

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

18707

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

18708

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

18709

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

18710

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

18711

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

18712

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

18713

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

18714

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

18715

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

18716

\[ {} 3 y+2 x +4-\left (4 x +6 y+5\right ) y^{\prime } = 0 \]

18717

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

18718

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

18719

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

18720

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

18721

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

18742

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

18743

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

18771

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

18968

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

18969

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

18970

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

18971

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

18972

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

18973

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

18974

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

18975

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

18976

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

18977

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

18978

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

18979

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

18980

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

18981

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

18982

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

18983

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

18984

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

18985

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

18986

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

18987

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

18988

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

18989

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

18990

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

18991

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

18992

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

18993

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

18994

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

18995

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

18996

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

18997

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

18998

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

18999

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

19000

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

19001

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

19002

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

19003

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

19004

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

19005

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

19006

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

19007

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

19008

\[ {} \left (6 x -5 y+4\right ) y^{\prime }+y-2 x -1 = 0 \]

19009

\[ {} \left (x -3 y+4\right ) y^{\prime }+7 y-5 x = 0 \]

19010

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

19011

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

19012

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

19013

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

19014

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

19015

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

19016

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

19017

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

19018

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

19019

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

19020

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

19021

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