6.202 Problems 20101 to 20200

Table 6.403: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

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

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

20152

\[ {} y^{\prime \prime }+3 y^{\prime }-54 y = 0 \]

20153

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

20154

\[ {} 2 y^{\prime \prime }+5 y^{\prime }-12 y = 0 \]

20155

\[ {} 9 y^{\prime \prime }+18 y^{\prime }-16 y = 0 \]

20156

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

20157

\[ {} y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-9 y^{\prime \prime }-11 y^{\prime }-4 y = 0 \]

20158

\[ {} y^{\prime \prime }+8 y^{\prime }+25 y = 0 \]

20159

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

20160

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

20161

\[ {} 6 y-5 y^{\prime }+y^{\prime \prime } = {\mathrm e}^{4 x} \]

20162

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

20163

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

20164

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

20165

\[ {} y^{\prime \prime \prime }+y = 3+{\mathrm e}^{-x}+5 \,{\mathrm e}^{2 x} \]

20166

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

20167

\[ {} y-2 y^{\prime }+y^{\prime \prime } = 3 \,{\mathrm e}^{\frac {5 x}{2}} \]

20168

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

20169

\[ {} y^{\prime \prime \prime }+8 y = x^{4}+2 x +1 \]

20170

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

20171

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

20172

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

20173

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

20174

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

20175

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

20176

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

20177

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

20178

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

20179

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

20180

\[ {} y^{\left (5\right )}-13 y^{\prime \prime \prime }+26 y^{\prime \prime }+82 y^{\prime }+104 y = 0 \]

20181

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

20182

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

20183

\[ {} 6 y-5 y^{\prime }+y^{\prime \prime } = x +{\mathrm e}^{m x} \]

20184

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

20185

\[ {} y^{\prime \prime \prime }-3 y^{\prime \prime }-6 y^{\prime }+8 y = x \]

20186

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

20187

\[ {} y^{\prime \prime \prime }-13 y^{\prime }+12 y = x \]

20188

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

20189

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

20190

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

20191

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

20192

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

20193

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

20194

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

20195

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

20196

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

20197

\[ {} y^{\prime \prime \prime }-7 y^{\prime }-6 y = {\mathrm e}^{2 x} \left (1+x \right ) \]

20198

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

20199

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

20200

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