5.3.8 Problems 701 to 800

Table 5.61: Problems not solved by Sympy

#

ODE

Mathematica

Maple

Sympy

4779

\[ {} x y^{\prime } = a \,x^{n}+b y+c y^{2} \]

4780

\[ {} x y^{\prime } = k +a \,x^{n}+b y+c y^{2} \]

4781

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

4788

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

4789

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

4790

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

4791

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

4793

\[ {} x y^{\prime } = a \,x^{m}-b y-c \,x^{n} y^{2} \]

4796

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

4809

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

4810

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

4811

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

4813

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

4815

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

4817

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

4818

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

4820

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

4821

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

4826

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

4827

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

4828

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

4832

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

4833

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

4834

\[ {} x y^{\prime } = y f \left (x^{m} y^{n}\right ) \]

4852

\[ {} 2 x y^{\prime }+1 = 4 i x y+y^{2} \]

4862

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

4878

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

4879

\[ {} x^{2} y^{\prime } = a +b \,x^{n}+x^{2} y^{2} \]

4881

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

4883

\[ {} x^{2} y^{\prime } = a +b \,x^{n}+c \,x^{2} y^{2} \]

4885

\[ {} x^{2} y^{\prime } = a +b x y+c \,x^{4} y^{2} \]

4888

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

4889

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

4892

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

4920

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

4923

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

4924

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

4931

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

4954

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

4959

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

4962

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

4967

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

4977

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

4988

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

4993

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

4996

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

5002

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

5005

\[ {} x^{7} y^{\prime }+5 y^{2} x^{3}+2 \left (x^{2}+1\right ) y^{3} = 0 \]

5006

\[ {} x^{n} y^{\prime } = a +b \,x^{n -1} y \]

5007

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

5008

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

5009

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

5010

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

5011

\[ {} x^{k} y^{\prime } = a \,x^{m}+b y^{n} \]

5020

\[ {} x^{{3}/{2}} y^{\prime } = a +b \,x^{{3}/{2}} y^{2} \]

5030

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

5034

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

5039

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

5040

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

5042

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

5051

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

5052

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

5059

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

5061

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

5071

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

5074

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

5075

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

5079

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

5087

\[ {} \left (x +2 y+1\right ) y^{\prime }+7+x -4 y = 0 \]

5093

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

5094

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

5095

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

5098

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

5109

\[ {} \left (6+3 x +5 y\right ) y^{\prime } = 2+x +7 y \]

5111

\[ {} \left (x +4 x^{3}+5 y\right ) y^{\prime }+7 x^{3}+3 x^{2} y+4 y = 0 \]

5115

\[ {} \left (1+x +9 y\right ) y^{\prime }+1+x +5 y = 0 \]

5119

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

5120

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

5122

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

5123

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

5124

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

5130

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

5131

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

5133

\[ {} y y^{\prime } x = a \,x^{n}+b y^{2} \]

5136

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

5144

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

5148

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

5151

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

5166

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

5170

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

5171

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

5176

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

5177

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

5181

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

5182

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

5183

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

5185

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

5200

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

5202

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

5203

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