4.9.10 Problems 901 to 1000

Table 4.643: First order ode linear in derivative

#

ODE

Mathematica

Maple

Sympy

2868

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

2869

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

2870

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

2871

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

2872

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

2873

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

2874

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

2875

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

2876

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

2877

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

2878

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

2879

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

2880

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

2881

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

2882

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

2883

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

2884

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

2885

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

2886

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

2887

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

2888

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

2889

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

2890

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

2891

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

2892

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

2893

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

2894

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

2895

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

2896

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

2897

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

2898

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

2899

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

2900

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

2901

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

2902

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

2903

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

2904

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

2905

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

2906

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

2907

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

2908

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

2909

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

2910

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

2911

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

2912

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

2913

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

2914

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

2915

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

2916

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

2917

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

2918

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

2919

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

2920

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

2921

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

2922

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

2923

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

2924

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

2925

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

2926

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

2927

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

2928

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

2929

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

2930

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

2931

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

2932

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

2933

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

2934

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

2935

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

2936

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

2937

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

2938

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

2939

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

2940

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

2941

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

2942

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

2943

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

2944

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

2945

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

2946

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

2947

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

2948

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

2949

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

2950

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

2951

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

2952

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

2953

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

2954

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

2955

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

2956

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

2957

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

2958

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

2959

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

2960

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

2961

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

2962

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

2963

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

2964

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

2965

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

2966

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

2967

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