2.2.273 Problems 27201 to 27300

Table 2.563: Main lookup table. Sorted sequentially by problem number.

#

ODE

CAS classification

Solved?

Maple

Mma

Sympy

time(sec)

27201

\begin{align*} y^{\prime }&=\frac {x^{2}}{2}+\frac {y^{2}}{2}-1 \\ \end{align*}

[_Riccati]

49.588

27202

\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=y-2 x \\ \end{align*}

[_linear]

2.034

27203

\begin{align*} y y^{\prime }+x&=0 \\ \end{align*}

[_separable]

5.293

27204

\begin{align*} x y^{\prime }&=2 y \\ \end{align*}

[_separable]

3.468

27205

\begin{align*} x y^{\prime }+y&=0 \\ \end{align*}

[_separable]

3.148

27206

\begin{align*} y^{\prime }+1&=2 \left (-x +y\right ) \left (y^{\prime }-1\right ) \\ \end{align*}

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

13.418

27207

\begin{align*} \left (1+y^{2}\right ) y^{\prime }+x&=0 \\ \end{align*}

[_separable]

1.746

27208

\begin{align*} y^{\prime }&=\frac {x}{y} \\ \end{align*}

[_separable]

5.177

27209

\begin{align*} y^{\prime }&=\frac {y-3 x}{x +3 y} \\ \end{align*}

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

10.222

27210

\begin{align*} y^{\prime }&=\frac {y}{x +y} \\ \end{align*}

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

10.907

27211

\begin{align*} x^{2}+y^{2} y^{\prime }&=1 \\ \end{align*}

[_separable]

2.113

27212

\begin{align*} \left (x^{2}+y^{2}\right ) y^{\prime }&=4 x \\ \end{align*}

[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]

1.757

27213

\begin{align*} \left (x +1\right ) y^{\prime }+y x&=0 \\ \end{align*}

[_separable]

2.802

27214

\begin{align*} \sqrt {1+y^{2}}&=x y y^{\prime } \\ \end{align*}

[_separable]

6.031

27215

\begin{align*} \left (x^{2}-1\right ) y^{\prime }+2 x y^{2}&=0 \\ y \left (0\right ) &= 1 \\ \end{align*}

[_separable]

7.161

27216

\begin{align*} \cot \left (x \right ) y^{\prime }+y&=2 \\ y \left (0\right ) &= -1 \\ \end{align*}

[_separable]

3.824

27217

\begin{align*} y^{\prime }&=3 y^{{2}/{3}} \\ y \left (2\right ) &= 0 \\ \end{align*}

[_quadrature]

1.529

27218

\begin{align*} x y^{\prime }+y&=y^{2} \\ y \left (1\right ) &= {\frac {1}{2}} \\ \end{align*}

[_separable]

3.440

27219

\begin{align*} 2 x^{2} y y^{\prime }+y^{2}&=2 \\ \end{align*}

[_separable]

3.301

27220

\begin{align*} y^{\prime }-x y^{2}&=2 y x \\ \end{align*}

[_separable]

2.710

27221

\begin{align*} {\mathrm e}^{-s} \left (1+s^{\prime }\right )&=1 \\ \end{align*}

[_quadrature]

0.966

27222

\begin{align*} z^{\prime }&=10^{x +z} \\ \end{align*}

[_separable]

2.804

27223

\begin{align*} x x^{\prime }+t&=1 \\ \end{align*}

[_separable]

2.460

27224

\begin{align*} y^{\prime }&=\cos \left (x -y\right ) \\ \end{align*}

[[_homogeneous, ‘class C‘], _dAlembert]

1.441

27225

\begin{align*} y^{\prime }-y&=2 x -3 \\ \end{align*}

[[_linear, ‘class A‘]]

1.070

27226

\begin{align*} \left (x +2 y\right ) y^{\prime }&=1 \\ y \left (0\right ) &= -1 \\ \end{align*}

[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert]

7.999

27227

\begin{align*} y^{\prime }&=\sqrt {4 x +2 y-1} \\ \end{align*}

[[_homogeneous, ‘class C‘], _dAlembert]

2.986

27228

\begin{align*} x^{2} y^{\prime }-2 \cos \left (2 y\right )&=1 \\ y \left (\infty \right ) &= \frac {9 \pi }{4} \\ \end{align*}

[_separable]

26.970

27229

\begin{align*} 3 y^{2} y^{\prime }+16 x&=2 x y^{3} \\ y \left (\infty \right ) &= y_{0} \\ \end{align*}

[_separable]

19.071

27230

\begin{align*} y^{\prime }&=\left (\frac {1+y^{2}}{x^{4}+1}\right )^{{1}/{3}} \\ \end{align*}

[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]

3.185

27231

\begin{align*} y^{\prime }&=\sqrt {\frac {\ln \left (y+1\right )}{\sin \left (x \right )}} \\ \end{align*}

[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]]

10.690

27232

\begin{align*} x +2 y-x y^{\prime }&=0 \\ \end{align*}

[_linear]

2.779

27233

\begin{align*} \left (x +y\right ) y^{\prime }+x -y&=0 \\ \end{align*}

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

11.902

27234

\begin{align*} y^{2}-2 y x +x^{2} y^{\prime }&=0 \\ \end{align*}

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

4.074

27235

\begin{align*} 2 x^{3} y^{\prime }&=\left (2 x^{2}-y^{2}\right ) y \\ \end{align*}

[[_homogeneous, ‘class A‘], _rational, _Bernoulli]

138.127

27236

\begin{align*} x^{2} y^{\prime }+y^{2}&=x y y^{\prime } \\ \end{align*}

[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

10.556

27237

\begin{align*} \left (x^{2}+y^{2}\right ) y^{\prime }&=2 y x \\ \end{align*}

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

16.550

27238

\begin{align*} x y^{\prime }-y&=x \tan \left (\frac {y}{x}\right ) \\ \end{align*}

[[_homogeneous, ‘class A‘], _dAlembert]

9.446

27239

\begin{align*} x y^{\prime }&=y-{\mathrm e}^{\frac {y}{x}} x \\ \end{align*}

[[_homogeneous, ‘class A‘], _dAlembert]

41.047

27240

\begin{align*} x y^{\prime }-y&=\left (x +y\right ) \ln \left (\frac {x +y}{x}\right ) \\ \end{align*}

[[_homogeneous, ‘class A‘], _dAlembert]

5.814

27241

\begin{align*} x y^{\prime }&=y \cos \left (\ln \left (\frac {y}{x}\right )\right ) \\ \end{align*}

[[_homogeneous, ‘class A‘], _dAlembert]

863.770

27242

\begin{align*} y+\sqrt {y x}&=x y^{\prime } \\ \end{align*}

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

8.526

27243

\begin{align*} x y^{\prime }&=y+\sqrt {x^{2}-y^{2}} \\ \end{align*}

[[_homogeneous, ‘class A‘], _rational, _dAlembert]

23.101

27244

\begin{align*} 2 x -4 y+1+\left (-3+x +y\right ) y^{\prime }&=0 \\ \end{align*}

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

20.234

27245

\begin{align*} 2 x +y+1-\left (4 x +2 y-3\right ) y^{\prime }&=0 \\ \end{align*}

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

8.005

27246

\begin{align*} x -y-1+\left (y-x +2\right ) y^{\prime }&=0 \\ \end{align*}

[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

12.279

27247

\begin{align*} \left (x +4 y\right ) y^{\prime }&=2 x +3 y-5 \\ \end{align*}

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

33.993

27248

\begin{align*} y+2&=\left (2 x +y-4\right ) y^{\prime } \\ \end{align*}

[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]]

11.506

27249

\begin{align*} y^{\prime }&=\frac {2 \left (y+2\right )^{2}}{\left (x +y-1\right )^{2}} \\ \end{align*}

[[_homogeneous, ‘class C‘], _rational]

4.654

27250

\begin{align*} \left (y^{\prime }+1\right ) \ln \left (\frac {x +y}{x +3}\right )&=\frac {x +y}{x +3} \\ \end{align*}

[[_homogeneous, ‘class C‘], _exact, _dAlembert]

34.667

27251

\begin{align*} y^{\prime }&=\frac {y+2}{x +1}+\tan \left (\frac {y-2 x}{x +1}\right ) \\ \end{align*}

[[_homogeneous, ‘class C‘], _dAlembert]

8.752

27252

\begin{align*} x^{3} \left (y^{\prime }-x \right )&=y^{2} \\ \end{align*}

[[_homogeneous, ‘class G‘], _rational, _Riccati]

3.253

27253

\begin{align*} 2 x^{2} y^{\prime }&=y^{3}+y x \\ \end{align*}

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

4.151

27254

\begin{align*} 2 x y^{\prime }+\left (x^{2} y^{4}+1\right ) y&=0 \\ \end{align*}

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

2.886

27255

\begin{align*} y+x \left (1+2 y x \right ) y^{\prime }&=0 \\ \end{align*}

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

23.783

27256

\begin{align*} 2 y^{\prime }+x&=4 \sqrt {y} \\ \end{align*}

[[_1st_order, _with_linear_symmetries], _Chini]

5.768

27257

\begin{align*} y^{\prime }&=y^{2}-\frac {2}{x^{2}} \\ \end{align*}

[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]]

5.911

27258

\begin{align*} 2 x y^{\prime }+y&=y^{2} \sqrt {x -x^{2} y^{2}} \\ \end{align*}

[[_homogeneous, ‘class G‘]]

8.512

27259

\begin{align*} \frac {2 x y y^{\prime }}{3}&=\sqrt {x^{6}-y^{4}}+y^{2} \\ \end{align*}

[[_homogeneous, ‘class G‘]]

17.480

27260

\begin{align*} 2 y+\left (x^{2} y+1\right ) x y^{\prime }&=0 \\ \end{align*}

[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]]

16.661

27261

\begin{align*} x y^{\prime }-2 y&=2 x^{4} \\ \end{align*}

[_linear]

3.343

27262

\begin{align*} \left (2 x +1\right ) y^{\prime }&=4 x +2 y \\ \end{align*}

[_linear]

1.897

27263

\begin{align*} y^{\prime }+y \tan \left (x \right )&=\sec \left (x \right ) \\ \end{align*}

[_linear]

1.593

27264

\begin{align*} x \left (y^{\prime }-y\right )&={\mathrm e}^{x} \\ \end{align*}

[[_linear, ‘class A‘]]

1.826

27265

\begin{align*} x^{2} y^{\prime }+y x +1&=0 \\ \end{align*}

[_linear]

1.379

27266

\begin{align*} y&=x \left (y^{\prime }-x \cos \left (x \right )\right ) \\ \end{align*}

[_linear]

1.769

27267

\begin{align*} y^{\prime }&=2 x \left (x^{2}+y\right ) \\ \end{align*}

[_linear]

1.652

27268

\begin{align*} \left (x y^{\prime }-1\right ) \ln \left (x \right )&=2 y \\ \end{align*}

[_linear]

1.369

27269

\begin{align*} x y^{\prime }+\left (x +1\right ) y&=3 x^{2} {\mathrm e}^{-x} \\ \end{align*}

[_linear]

2.153

27270

\begin{align*} \left (x +y^{2}\right ) y^{\prime }&=y \\ \end{align*}

[[_homogeneous, ‘class G‘], _rational]

2.286

27271

\begin{align*} \left (2 \,{\mathrm e}^{y}-x \right ) y^{\prime }&=1 \\ \end{align*}

[[_1st_order, _with_exponential_symmetries]]

4.608

27272

\begin{align*} \left (\sin \left (y\right )^{2}+x \cot \left (y\right )\right ) y^{\prime }&=1 \\ \end{align*}

[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]

2.444

27273

\begin{align*} \left (2 x +y\right ) y^{\prime }&=y+4 \ln \left (y\right ) y^{\prime } \\ \end{align*}

[[_1st_order, _with_linear_symmetries]]

1.982

27274

\begin{align*} y^{\prime }&=\frac {y}{3 x -y^{2}} \\ \end{align*}

[[_homogeneous, ‘class G‘], _rational]

3.349

27275

\begin{align*} \left (1-2 y x \right ) y^{\prime }&=y \left (-1+y\right ) \\ \end{align*}

[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]]

5.463

27276

\begin{align*} 2 y+y^{\prime }&=y^{2} {\mathrm e}^{x} \\ \end{align*}

[[_1st_order, _with_linear_symmetries], _Bernoulli]

1.178

27277

\begin{align*} \left (x +1\right ) \left (y^{\prime }+y^{2}\right )&=-y \\ \end{align*}

[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli]

1.639

27278

\begin{align*} y^{\prime }&=y^{4} \cos \left (x \right )+y \tan \left (x \right ) \\ \end{align*}

[_Bernoulli]

3.320

27279

\begin{align*} x y^{2} y^{\prime }&=x^{2}+y^{3} \\ \end{align*}

[[_homogeneous, ‘class D‘], _rational, _Bernoulli]

2.778

27280

\begin{align*} x y y^{\prime }&=x +y^{2} \\ \end{align*}

[[_homogeneous, ‘class D‘], _rational, _Bernoulli]

3.394

27281

\begin{align*} x y^{\prime }-2 x^{2} \sqrt {y}&=4 y \\ \end{align*}

[[_homogeneous, ‘class G‘], _rational, _Bernoulli]

2.726

27282

\begin{align*} x y^{\prime }+2 y+x^{5} y^{3} {\mathrm e}^{x}&=0 \\ \end{align*}

[_Bernoulli]

1.951

27283

\begin{align*} 2 y^{\prime }-\frac {x}{y}&=\frac {x y}{x^{2}-1} \\ \end{align*}

[_rational, _Bernoulli]

2.331

27284

\begin{align*} y^{\prime } x^{3} \sin \left (y\right )&=x y^{\prime }-2 y \\ \end{align*}

[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]

1.960

27285

\begin{align*} \left (2 x^{2} y \ln \left (y\right )-x \right ) y^{\prime }&=y \\ \end{align*}

[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]]

3.086

27286

\begin{align*} x&=\left (x^{2}-2 y+1\right ) y^{\prime } \\ \end{align*}

[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]]

1.877

27287

\begin{align*} \left (x +1\right ) \left (y y^{\prime }-1\right )&=y^{2} \\ \end{align*}

[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli]

2.611

27288

\begin{align*} x \left ({\mathrm e}^{y}-y^{\prime }\right )&=2 \\ \end{align*}

[[_1st_order, _with_linear_symmetries]]

1.834

27289

\begin{align*} \left (x^{2}-1\right ) y^{\prime } \sin \left (y\right )+2 x \cos \left (y\right )&=-2 x^{3}+2 x \\ \end{align*}

[‘y=_G(x,y’)‘]

3.731

27290

\begin{align*} x^{2} y^{\prime }+y x +x^{2} y^{2}&=4 \\ \end{align*}

[[_homogeneous, ‘class G‘], _rational, _Riccati]

4.691

27291

\begin{align*} 3 y^{\prime }+y^{2}+\frac {2}{x^{2}}&=0 \\ \end{align*}

[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]]

3.141

27292

\begin{align*} x y^{\prime }-\left (2 x +1\right ) y+y^{2}&=-x^{2} \\ \end{align*}

[[_homogeneous, ‘class D‘], _rational, _Riccati]

1.292

27293

\begin{align*} y^{\prime }-2 y x +y^{2}&=-x^{2}+5 \\ \end{align*}

[[_homogeneous, ‘class C‘], _Riccati]

6.125

27294

\begin{align*} y^{\prime }+2 y \,{\mathrm e}^{x}-y^{2}&={\mathrm e}^{x}+{\mathrm e}^{2 x} \\ \end{align*}

[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati]

10.431

27295

\begin{align*} y^{\prime } \sin \left (2 x \right )&=2 y+2 \cos \left (x \right ) \\ y \left (\frac {\pi }{2}\right ) &= 0 \\ \end{align*}

[_linear]

14.400

27296

\begin{align*} x^{\prime }+x&=f \left (t \right ) \\ \end{align*}

[[_linear, ‘class A‘]]

1.580

27297

\begin{align*} x^{\prime }+a \left (t \right ) x&=f \left (t \right ) \\ \end{align*}

[_linear]

1.749

27298

\begin{align*} x^{\prime }+a \left (t \right ) x&=f \left (t \right ) \\ x \left (0\right ) &= b \\ \end{align*}

[_linear]

1.806

27299

\begin{align*} x y^{\prime }-\left (2 x^{2}+1\right ) y&=x^{2} \\ \end{align*}

[_linear]

1.529

27300

\begin{align*} 2 y x +\left (x^{2}-y^{2}\right ) y^{\prime }&=0 \\ \end{align*}

[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert]

54.755