5.1.22 Problems 2101 to 2200

Table 5.43: First order ode

#

ODE

Mathematica

Maple

5016

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

5017

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

5018

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

5019

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

5020

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

5021

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

5022

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

5023

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

5024

\[ {}y y^{\prime } = \operatorname {a0} +\operatorname {a1} y+\operatorname {a2} y^{2} \]

5025

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

5026

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

5027

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

5028

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

5029

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

5030

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

5031

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

5032

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

5033

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

5034

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

5035

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

5036

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

5037

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

5038

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

5039

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

5040

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

5041

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

5042

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

5043

\[ {}\left (y-x +3\right ) y^{\prime } = 11-4 x +3 y \]

5044

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

5045

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

5046

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

5047

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

5048

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

5049

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

5050

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

5051

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

5052

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

5053

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

5054

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

5055

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

5056

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

5057

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

5058

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

5059

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

5060

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

5061

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

5062

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

5063

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

5064

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

5065

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

5066

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

5067

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

5068

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

5069

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

5070

\[ {}\left (19+9 x +2 y\right ) y^{\prime }+18-2 x -6 y = 0 \]

5071

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

5072

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

5073

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

5074

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

5075

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

5076

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

5077

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

5078

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

5079

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

5080

\[ {}\left (1+9 x -3 y\right ) y^{\prime }+2+3 x -y = 0 \]

5081

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

5082

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

5083

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

5084

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

5085

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

5086

\[ {}\left (11-11 x -4 y\right ) y^{\prime } = 62-8 x -25 y \]

5087

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

5088

\[ {}\left (7 x +5 y\right ) y^{\prime }+10 x +8 y = 0 \]

5089

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

5090

\[ {}\left (5-x +6 y\right ) y^{\prime } = 3-x +4 y \]

5091

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

5092

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

5093

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

5094

\[ {}\left (8+5 x -12 y\right ) y^{\prime } = 3+2 x -5 y \]

5095

\[ {}\left (140+7 x -16 y\right ) y^{\prime }+25+8 x +y = 0 \]

5096

\[ {}\left (3+9 x +21 y\right ) y^{\prime } = 45+7 x -5 y \]

5097

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

5098

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

5099

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

5100

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

5101

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

5102

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

5103

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

5104

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

5105

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

5106

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

5107

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

5108

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

5109

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

5110

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

5111

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

5112

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

5113

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

5114

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

5115

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