3.1.29 Problems 2801 to 2900

Table 3.57: First order ode

#

ODE

Mathematica

Maple

4939

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

4940

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

4941

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

4942

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

4943

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

4944

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

4945

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

4946

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

4947

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

4948

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

4949

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

4950

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

4951

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

4952

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

4953

\[ {}3 t = {\mathrm e}^{t} y^{\prime }+y \ln \left (t \right ) \]

4954

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

4955

\[ {}3 r = r^{\prime }-\theta ^{3} \]

4956

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

4957

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

4958

\[ {}r^{\prime }+r \tan \left (\theta \right ) = \sec \left (\theta \right ) \]

4959

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

4960

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

4961

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

4962

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

4963

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

4964

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

4965

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

4966

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

4967

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

4968

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

4969

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

4970

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

4971

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

4972

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

4973

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

4974

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

4975

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

4976

\[ {}x^{\prime } = \alpha -\beta \cos \left (\frac {\pi t}{12}\right )-k x \]

4977

\[ {}u^{\prime } = \alpha \left (1-u\right )-\beta u \]

4978

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

4979

\[ {}x^{\frac {10}{3}}-2 y+x y^{\prime } = 0 \]

4980

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

4981

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

4982

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

4983

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

4984

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

4985

\[ {}\theta r^{\prime }+3 r-\theta -1 = 0 \]

4986

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

4987

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

4988

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

4989

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

4990

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

4991

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

4992

\[ {}\cos \left (\theta \right ) r^{\prime }-r \sin \left (\theta \right )+{\mathrm e}^{\theta } = 0 \]

4993

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

4994

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

4995

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

4996

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

4997

\[ {}y^{\prime }-4 y = 32 x^{2} \]

4998

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

4999

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

5000

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

5001

\[ {}t^{3} y^{2}+\frac {t^{4} y^{\prime }}{y^{6}} = 0 \]

5055

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

5056

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

5057

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

5058

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

5059

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

5060

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

5061

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

5062

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

5063

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

5072

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

5073

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

5075

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

5076

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

5077

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

5078

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

5079

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

5080

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

5081

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

5082

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

5083

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

5084

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

5085

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

5086

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

5087

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

5088

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

5089

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

5090

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

5091

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

5092

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

5093

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

5094

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

5095

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

5096

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

5097

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

5098

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

5099

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

5100

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