4.1.83 Problems 8201 to 8300

Table 4.165: First order ode

#

ODE

Mathematica

Maple

Sympy

19066

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

19067

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

19068

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

19069

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

19070

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

19071

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

19072

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

19073

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

19074

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

19075

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

19076

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

19077

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

19078

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

19079

\[ {} y^{\prime }+\frac {a x +b y+c}{b x +f y+e} = 0 \]

19132

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

19133

\[ {} {y^{\prime }}^{2}-5 y^{\prime }+6 = 0 \]

19134

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

19135

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

19136

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

19137

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

19138

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

19139

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

19140

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

19141

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

19142

\[ {} {y^{\prime }}^{3}-a \,x^{4} = 0 \]

19143

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

19144

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

19145

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

19146

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

19147

\[ {} x^{2} {y^{\prime }}^{2}+x y y^{\prime }-6 y^{2} = 0 \]

19148

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

19149

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

19150

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

19151

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

19152

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

19153

\[ {} 3 {y^{\prime }}^{5}-y y^{\prime }+1 = 0 \]

19154

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

19155

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

19156

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

19157

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

19158

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

19159

\[ {} y = y^{\prime } \tan \left (y^{\prime }\right )+\ln \left (\cos \left (y^{\prime }\right )\right ) \]

19160

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

19161

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

19162

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

19163

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

19164

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

19165

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

19166

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

19167

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

19168

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

19169

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

19170

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

19171

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

19172

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

19173

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

19174

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

19175

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

19176

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

19177

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

19178

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

19179

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

19180

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

19181

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

19182

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

19183

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

19184

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

19185

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

19186

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

19187

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

19188

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

19189

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

19190

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

19191

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

19192

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

19193

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

19194

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

19195

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

19196

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

19197

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

19198

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

19199

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

19200

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

19201

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

19202

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

19203

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

19204

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

19205

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

19206

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

19207

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

19208

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

19209

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

19210

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

19211

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

19212

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

19213

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

19214

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

19215

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

19216

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

19217

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