4.9.30 Problems 2901 to 3000

Table 4.897: First order ode linear in derivative

#

ODE

Mathematica

Maple

Sympy

7760

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

7761

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

7762

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

7763

\[ {} \frac {r \tan \left (\theta \right ) r^{\prime }}{a^{2}-r^{2}} = 1 \]

7764

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

7765

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

7802

\[ {} y^{\prime }-5 y = \left (x -1\right ) \sin \left (x \right )+\left (1+x \right ) \cos \left (x \right ) \]

7803

\[ {} y^{\prime }-5 y = 3 \,{\mathrm e}^{x}-2 x +1 \]

7804

\[ {} y^{\prime }-5 y = x^{2} {\mathrm e}^{x}-x \,{\mathrm e}^{5 x} \]

7810

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

7811

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

7812

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

7820

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

7829

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

7830

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

7831

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

7832

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

7856

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

7857

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

7859

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

7866

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

7867

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

7868

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

7869

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

7870

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

7871

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

7872

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

7873

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

7874

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

7875

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

7876

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

7877

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

7878

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

7879

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

7880

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

7881

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

7882

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

7883

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

7884

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

7885

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

7886

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

7887

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

7888

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

7889

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

7890

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

7891

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

7892

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

7893

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

7894

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

7895

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

7896

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

7897

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

7898

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

7899

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

7900

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

7901

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

7902

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

7903

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

7904

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

7905

\[ {} 1-\sqrt {a^{2}-x^{2}}\, y^{\prime } = 0 \]

7906

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

7907

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

7908

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

7909

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

7910

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

7911

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

7912

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

7913

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

7914

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

7915

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

7916

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

7917

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

7918

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

7919

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

7920

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

7921

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

7922

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

7923

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

7924

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

7925

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

7926

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

7927

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

7928

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

7929

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

7930

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

7931

\[ {} i^{\prime }-6 i = 10 \sin \left (2 t \right ) \]

7932

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

7933

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

7934

\[ {} \left (2 s-{\mathrm e}^{2 t}\right ) s^{\prime } = 2 s \,{\mathrm e}^{2 t}-2 \cos \left (2 t \right ) \]

7935

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

7936

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

7937

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

7938

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

7939

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

7940

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

7941

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

7942

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

7943

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

7944

\[ {} 2 x y^{5}-y+2 x y^{\prime } = 0 \]

7945

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