5.3.21 Problems 2001 to 2100

Table 5.87: Problems not solved by Sympy

#

ODE

Mathematica

Maple

Sympy

8071

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

8072

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

8076

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

8079

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

8087

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

8096

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

8102

\[ {} x^{3} \left (1+x \right ) y^{\prime \prime \prime }-\left (4 x +2\right ) x^{2} y^{\prime \prime }+\left (4+10 x \right ) x y^{\prime }-\left (4+12 x \right ) y = 0 \]

8103

\[ {} x^{3} \left (x^{2}+1\right ) y^{\prime \prime \prime }-\left (4 x^{2}+2\right ) x^{2} y^{\prime \prime }+\left (10 x^{2}+4\right ) x y^{\prime }-\left (12 x^{2}+4\right ) y = 0 \]

8104

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

8107

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

8119

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

8123

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

8124

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}+\frac {9}{4}\right ) y = 0 \]

8125

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}+\frac {25}{4}\right ) y = 0 \]

8129

\[ {} x^{3} y^{\prime \prime }+y = \frac {1}{x^{4}} \]

8130

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

8131

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

8142

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

8143

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

8144

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

8145

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

8148

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

8150

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

8155

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

8157

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

8159

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

8162

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

8163

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

8164

\[ {} t^{5} y^{\prime \prime \prime \prime }-t^{3} y^{\prime \prime }+6 y = 0 \]

8165

\[ {} u^{\prime \prime }+u^{\prime }+u = \cos \left (r +u\right ) \]

8166

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

8168

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

8170

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

8207

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

8234

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

8243

\[ {} y^{\prime } = \sqrt {y^{2}-9} \]

8246

\[ {} y^{\prime } = \sqrt {y^{2}-9} \]

8247

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

8251

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

8257

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

8262

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

8264

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

8265

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

8267

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

8279

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

8281

\[ {} y^{\prime } = 6 \sqrt {y}+5 x^{3} \]

8288

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

8292

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

8300

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

8301

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

8302

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

8303

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

8304

\[ {} y^{\prime } = {\mathrm e}^{-\frac {x y^{2}}{100}} \]

8305

\[ {} y^{\prime } = {\mathrm e}^{-\frac {x y^{2}}{100}} \]

8306

\[ {} y^{\prime } = {\mathrm e}^{-\frac {x y^{2}}{100}} \]

8307

\[ {} y^{\prime } = {\mathrm e}^{-\frac {x y^{2}}{100}} \]

8333

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

8334

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

8375

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

8387

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

8388

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

8389

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

8390

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

8391

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

8395

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

8419

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

8424

\[ {} y^{\prime } = -\frac {5+8 x}{3 y^{2}+1} \]

8425

\[ {} y^{\prime } = -\frac {5+8 x}{3 y^{2}+1} \]

8426

\[ {} y^{\prime } = -\frac {5+8 x}{3 y^{2}+1} \]

8427

\[ {} y^{\prime } = -\frac {5+8 x}{3 y^{2}+1} \]

8445

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

8467

\[ {} 2 y+y^{\prime } = \left \{\begin {array}{cc} 1 & 0\le x \le 3 \\ 0 & 3<x \end {array}\right . \]

8468

\[ {} y^{\prime }+y = \left \{\begin {array}{cc} 1 & 0\le x \le 1 \\ -1 & 1<x \end {array}\right . \]

8469

\[ {} y^{\prime }+2 x y = \left \{\begin {array}{cc} x & 0\le x <1 \\ 0 & 1\le x \end {array}\right . \]

8470

\[ {} \left (x^{2}+1\right ) y^{\prime }+2 x y = \left \{\begin {array}{cc} x & 0\le x <1 \\ -x & 1\le x \end {array}\right . \]

8471

\[ {} y^{\prime }+\left (\left \{\begin {array}{cc} 2 & 0\le x \le 1 \\ -\frac {2}{x} & 1<x \end {array}\right .\right ) y = 4 x \]

8472

\[ {} y^{\prime }+\left (\left \{\begin {array}{cc} 1 & 0\le x \le 2 \\ 5 & 2<x \end {array}\right .\right ) y = 0 \]

8481

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

8482

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

8497

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

8510

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

8515

\[ {} x^{2} \left (x -5\right )^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}-25\right ) y = 0 \]

8518

\[ {} x^{3} \left (x^{2}-25\right ) \left (x -2\right )^{2} y^{\prime \prime }+3 x \left (x -2\right ) y^{\prime }+7 \left (x +5\right ) y = 0 \]

8540

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

8542

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

8543

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

8544

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

8554

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\left (2 x^{2}-64\right ) y = 0 \]

8558

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

8579

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

8614

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

8622

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

8625

\[ {} \left (x -1\right )^{2} y^{\prime \prime }-\left (x -1\right ) y^{\prime }-35 y = 0 \]

8626

\[ {} 16 \left (1+x \right )^{2} y^{\prime \prime }+3 y = 0 \]

8627

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

8652

\[ {} y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 4 t & 0<t <1 \\ 8 & 1<t \end {array}\right . \]

8653

\[ {} y^{\prime \prime }+y^{\prime }-2 y = \left \{\begin {array}{cc} 3 \sin \left (t \right )-\cos \left (t \right ) & 0<t <2 \pi \\ 3 \sin \left (2 t \right )-\cos \left (2 t \right ) & 2 \pi <t \end {array}\right . \]

8654

\[ {} y^{\prime \prime }+3 y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0<t <1 \\ 0 & 1<t \end {array}\right . \]

8656

\[ {} y^{\prime \prime }+2 y^{\prime }+5 y = \left \{\begin {array}{cc} 10 \sin \left (t \right ) & 0<t <2 \pi \\ 0 & 2 \pi <t \end {array}\right . \]

8698

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