5.3.56 Problems 5501 to 5600

Table 5.145: Problems not solved by Sympy

#

ODE

Mathematica

Maple

Sympy

18985

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

18986

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

19006

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

19016

\[ {} \left (6 x -5 y+4\right ) y^{\prime }+y-2 x -1 = 0 \]

19026

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

19030

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

19041

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

19042

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

19046

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

19047

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

19053

\[ {} \left (20 x^{2}+8 x y+4 y^{2}+3 y^{3}\right ) y+4 \left (x^{2}+x y+y^{2}+y^{3}\right ) x y^{\prime } = 0 \]

19054

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

19055

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

19056

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

19061

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

19064

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

19066

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

19067

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

19068

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

19069

\[ {} {x^{\prime }}^{2} = k^{2} \left (1-{\mathrm e}^{-\frac {2 g x}{k^{2}}}\right ) \]

19072

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

19073

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

19074

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

19081

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

19084

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

19085

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

19086

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

19087

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

19154

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

19159

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

19161

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

19162

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

19164

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

19165

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

19167

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

19168

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

19169

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

19171

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

19174

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

19175

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

19177

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

19178

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

19179

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

19180

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

19181

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

19182

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

19183

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

19184

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

19188

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

19190

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

19192

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

19193

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

19196

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

19198

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

19199

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

19201

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

19203

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

19206

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

19207

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

19209

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

19210

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

19211

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

19213

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

19217

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

19218

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

19223

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

19226

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

19227

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

19228

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

19230

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

19231

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

19232

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

19233

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

19234

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

19235

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

19236

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

19237

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

19238

\[ {} 8 x {y^{\prime }}^{3} = y \left (12 {y^{\prime }}^{2}-9\right ) \]

19240

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

19243

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

19274

\[ {} \left (5+2 x \right )^{2} y^{\prime \prime }-6 \left (5+2 x \right ) y^{\prime }+8 y = 0 \]

19276

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

19277

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

19278

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

19280

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

19281

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

19282

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

19283

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

19284

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

19285

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

19286

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

19287

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

19288

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

19289

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

19290

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

19291

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

19292

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

19294

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

19306

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

19307

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