4.1.59 Problems 5801 to 5900

Table 4.117: First order ode

#

ODE

Mathematica

Maple

Sympy

12803

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

12804

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

12805

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

12806

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

12807

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

12808

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

12809

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

12810

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

12811

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

12812

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

12813

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

12814

\[ {} 4 \,{\mathrm e}^{2 y} {y^{\prime }}^{2}+2 x y^{\prime }-1 = 0 \]

12815

\[ {} 4 \,{\mathrm e}^{2 y} {y^{\prime }}^{2}+2 \,{\mathrm e}^{2 x} y^{\prime }-{\mathrm e}^{2 x} = 0 \]

12816

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

12817

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

12818

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

12819

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

12820

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

12821

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

12822

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

12823

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

12824

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

12825

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

12826

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

12827

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

12828

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

12829

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

12830

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

12831

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

12832

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

12833

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

12834

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

12835

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

12836

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

12837

\[ {} 8 \left (1+y^{\prime }\right )^{3} = 27 \left (x +y\right ) \left (1-y^{\prime }\right )^{3} \]

12838

\[ {} 4 {y^{\prime }}^{2} = 9 x \]

12839

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

12946

\[ {} x^{\prime } = \frac {2 x}{t} \]

12947

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

12948

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

12950

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

12951

\[ {} x^{\prime }+2 x = t^{2}+4 t +7 \]

12952

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

12955

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

12956

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

12957

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

12958

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

12960

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

12961

\[ {} x^{\prime } = \frac {1}{t \ln \left (t \right )} \]

12962

\[ {} \sqrt {t}\, x^{\prime } = \cos \left (\sqrt {t}\right ) \]

12963

\[ {} x^{\prime } = \frac {{\mathrm e}^{-t}}{\sqrt {t}} \]

12965

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

12966

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

12967

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

12968

\[ {} u^{\prime } = \frac {1}{5-2 u} \]

12969

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

12970

\[ {} Q^{\prime } = \frac {Q}{4+Q^{2}} \]

12971

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

12972

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

12973

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

12974

\[ {} \theta ^{\prime } = t \sqrt {t^{2}+1}\, \sec \left (\theta \right ) \]

12975

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

12976

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

12977

\[ {} y^{\prime }+y+\frac {1}{y} = 0 \]

12978

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

12979

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

12980

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

12981

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

12982

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

12983

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

12984

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

12985

\[ {} T^{\prime } = 2 a t \left (T^{2}-a^{2}\right ) \]

12986

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

12987

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

12988

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

12989

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

12990

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

12991

\[ {} x^{\prime } = \frac {4 t^{2}+3 x^{2}}{2 t x} \]

12992

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

12994

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

12995

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

12996

\[ {} x^{\prime } = 2 t^{3} x-6 \]

12997

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

12998

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

12999

\[ {} 7 t^{2} x^{\prime } = 3 x-2 t \]

13000

\[ {} x x^{\prime } = 1-t x \]

13001

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

13002

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

13003

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

13004

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

13005

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

13006

\[ {} \theta ^{\prime } = -a \theta +{\mathrm e}^{b t} \]

13007

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

13008

\[ {} x^{\prime }+\frac {5 x}{t} = t +1 \]

13009

\[ {} x^{\prime } = \left (a +\frac {b}{t}\right ) x \]

13010

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

13011

\[ {} N^{\prime } = N-9 \,{\mathrm e}^{-t} \]

13012

\[ {} \cos \left (\theta \right ) v^{\prime }+v = 3 \]

13013

\[ {} R^{\prime } = \frac {R}{t}+t \,{\mathrm e}^{-t} \]

13014

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