4.1.83 Problems 8201 to 8300

Table 4.165: First order ode

#

ODE

Mathematica

Maple

Sympy

20070

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

20071

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

20072

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

20073

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

20074

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

20075

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

20076

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

20077

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

20078

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

20079

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

20080

\[ {} 3 y+2 x +4-\left (4 x +6 y+5\right ) y^{\prime } = 0 \]

20081

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

20082

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

20083

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

20084

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

20085

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

20086

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

20087

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

20088

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

20089

\[ {} {y^{\prime }}^{3} = a \,x^{4} \]

20090

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

20091

\[ {} {y^{\prime }}^{2}-7 y^{\prime }+12 = 0 \]

20092

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

20093

\[ {} y = -a y^{\prime }+\frac {c +a \arcsin \left (y^{\prime }\right )}{\sqrt {1-{y^{\prime }}^{2}}} \]

20094

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

20095

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

20096

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

20097

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

20098

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

20099

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

20100

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

20101

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

20102

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

20103

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

20104

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

20105

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

20106

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

20107

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

20108

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

20109

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

20110

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

20111

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

20112

\[ {} {y^{\prime }}^{2}-9 y^{\prime }+18 = 0 \]

20113

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

20114

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

20115

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

20116

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

20117

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

20118

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

20119

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

20120

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

20121

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

20122

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

20123

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

20124

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

20125

\[ {} {y^{\prime }}^{3}-4 y y^{\prime } x +8 y^{2} = 0 \]

20126

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

20127

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

20128

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

20129

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

20130

\[ {} y-\frac {1}{\sqrt {1+{y^{\prime }}^{2}}} = b \]

20131

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

20132

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

20133

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

20134

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

20135

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

20136

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

20137

\[ {} \left (1+y^{\prime }\right )^{3} = \frac {7 \left (x +y\right ) \left (1-y^{\prime }\right )^{3}}{4 a} \]

20138

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

20139

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

20140

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

20141

\[ {} a {y^{\prime }}^{3} = 27 y \]

20142

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

20143

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

20144

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

20145

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

20146

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

20147

\[ {} 4 {y^{\prime }}^{2} = 9 x \]

20148

\[ {} 4 x \left (x -1\right ) \left (x -2\right ) {y^{\prime }}^{2}-\left (3 x^{2}-6 x +2\right )^{2} = 0 \]

20149

\[ {} \left (8 {y^{\prime }}^{3}-27\right ) x = 12 y {y^{\prime }}^{2} \]

20150

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

20151

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

20332

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

20333

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

20334

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

20335

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

20336

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

20337

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

20338

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

20339

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

20340

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

20341

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

20342

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

20343

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

20344

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

20345

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

20346

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

20347

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

20348

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

20349

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