2.3.243 Problems 24201 to 24300

Table 2.1029: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

24201

19233

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

26.466

24202

14451

\begin{align*} {\mathrm e}^{x} y+2 \,{\mathrm e}^{x}+y^{2}+\left ({\mathrm e}^{x}+2 y x \right ) y^{\prime }&=0 \\ y \left (0\right ) &= 6 \\ \end{align*}

26.496

24203

4318

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

26.540

24204

14896

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

26.550

24205

12053

\begin{align*} y^{\prime }&=\frac {-4 a x y-a^{2} x^{3}-2 a b \,x^{2}-4 a x +8}{8 y+2 a \,x^{2}+4 b x +8} \\ \end{align*}

26.575

24206

3961

\begin{align*} y^{\prime }-3 y&=-10 \,{\mathrm e}^{-t +a} \sin \left (-2 t +2 a \right ) \operatorname {Heaviside}\left (t -a \right ) \\ y \left (0\right ) &= 5 \\ \end{align*}
Using Laplace transform method.

26.599

24207

25443

\begin{align*} y^{\prime }-3 y&=5 \,{\mathrm e}^{2 i t} \\ \end{align*}

26.635

24208

12381

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

26.640

24209

13809

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

26.660

24210

13494

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

26.669

24211

12330

\begin{align*} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+\left (\operatorname {a1} \,x^{2}+\operatorname {b1} x +\operatorname {c1} \right ) y&=0 \\ \end{align*}

26.684

24212

12673

\begin{align*} y^{\prime \prime }&=-\frac {\left (a p \,x^{b}+q \right ) y^{\prime }}{x \left (a \,x^{b}-1\right )}-\frac {\left (a r \,x^{b}+s \right ) y}{x^{2} \left (a \,x^{b}-1\right )} \\ \end{align*}

26.686

24213

6815

\begin{align*} y^{\prime }&=\frac {-3+x +y}{x -y-1} \\ \end{align*}

26.712

24214

21433

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

26.715

24215

11512

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

26.716

24216

17264

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

26.720

24217

18575

\begin{align*} {\mathrm e}^{x} \sin \left (y\right )+3 y-\left (3 x -{\mathrm e}^{x} \sin \left (y\right )\right ) y^{\prime }&=0 \\ \end{align*}

26.735

24218

1666

\begin{align*} y^{\prime }&=\frac {-6 x +y-3}{2 x -y-1} \\ \end{align*}

26.776

24219

17230

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

26.789

24220

11755

\begin{align*} y {y^{\prime }}^{2}-4 a^{2} x y^{\prime }+a^{2} y&=0 \\ \end{align*}

26.841

24221

5476

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

26.855

24222

4280

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

26.871

24223

12555

\begin{align*} 48 x \left (x -1\right ) y^{\prime \prime }+\left (152 x -40\right ) y^{\prime }+53 y&=0 \\ \end{align*}

26.875

24224

14909

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

26.886

24225

14506

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

26.906

24226

25025

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

26.916

24227

5551

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

26.918

24228

6905

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

26.941

24229

25750

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

26.952

24230

24285

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

26.961

24231

22328

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

26.962

24232

12087

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

26.965

24233

7472

\begin{align*} 5 x^{2} y+6 x^{3} y^{2}+4 x y^{2}+\left (2 x^{3}+3 x^{4} y+3 x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}

26.966

24234

21810

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

26.973

24235

4665

\begin{align*} y^{\prime }&=\left (1+4 x +9 y\right )^{2} \\ \end{align*}

26.976

24236

6835

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

26.983

24237

3478

\begin{align*} \left (5 x +y-7\right ) y^{\prime }&=3 x +3 y+3 \\ \end{align*}

26.990

24238

14535

\begin{align*} 3 x^{2}+2 x y^{2}+\left (2 x^{2} y+6 y^{2}\right ) y^{\prime }&=0 \\ y \left (1\right ) &= 2 \\ \end{align*}

27.003

24239

15151

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

27.014

24240

2888

\begin{align*} y^{\prime }&=\frac {y}{x}+\tan \left (\frac {y}{x}\right ) \\ y \left (6\right ) &= \pi \\ \end{align*}

27.023

24241

17114

\begin{align*} y^{\prime }&={\mathrm e}^{t -y} \\ y \left (0\right ) &= 0 \\ \end{align*}

27.043

24242

20594

\begin{align*} y^{\prime \prime }&=\frac {1}{\sqrt {a y}} \\ \end{align*}

27.053

24243

3546

\begin{align*} y^{\prime } x&=\sqrt {16 x^{2}-y^{2}}+y \\ \end{align*}

27.070

24244

25748

\begin{align*} y^{\prime }&=6 \sqrt {y}+5 x^{3} \\ y \left (-1\right ) &= 4 \\ \end{align*}

27.074

24245

1677

\begin{align*} y^{\prime }+\frac {2 y}{x}&=\frac {3 y^{2} x^{2}+6 y x +2}{x^{2} \left (2 y x +3\right )} \\ y \left (2\right ) &= 2 \\ \end{align*}

27.081

24246

24866

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

27.085

24247

1147

\begin{align*} \sin \left (2 x \right )+\cos \left (3 y\right ) y^{\prime }&=0 \\ y \left (\frac {\pi }{2}\right ) &= 0 \\ \end{align*}

27.095

24248

8119

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

27.134

24249

13309

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

27.156

24250

17872

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

27.168

24251

1718

\begin{align*} 6 x y^{2}+2 y+\left (12 x^{2} y+6 x +3\right ) y^{\prime }&=0 \\ \end{align*}

27.187

24252

23222

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

27.212

24253

2348

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

27.220

24254

16231

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

27.250

24255

6442

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

27.273

24256

5073

\begin{align*} \left (1+5 x -y\right ) y^{\prime }+5+x -5 y&=0 \\ \end{align*}

27.296

24257

21814

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

27.300

24258

12155

\begin{align*} y^{\prime }&=-\frac {-y x -y+x^{5} \sqrt {x^{2}+y^{2}}-x^{4} \sqrt {x^{2}+y^{2}}\, y}{x \left (x +1\right )} \\ \end{align*}

27.311

24259

19725

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

27.312

24260

23150

\begin{align*} y^{\prime }&=\frac {\left (a -x \right ) y}{d \,x^{2}+c x +b} \\ \end{align*}

27.312

24261

24318

\begin{align*} y^{\prime }&=\left (9 x +4 y+1\right )^{2} \\ \end{align*}

27.353

24262

6913

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

27.362

24263

13802

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

27.372

24264

17287

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

27.401

24265

6831

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

27.426

24266

16153

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

27.428

24267

16286

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

27.448

24268

6805

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

27.499

24269

6909

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

27.543

24270

14554

\begin{align*} 2 x +3 y+1+\left (4 x +6 y+1\right ) y^{\prime }&=0 \\ y \left (-2\right ) &= 2 \\ \end{align*}

27.547

24271

15568

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

27.564

24272

18553

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

27.565

24273

23961

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

27.580

24274

4289

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

27.593

24275

20011

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

27.595

24276

13331

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

27.599

24277

25852

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

27.605

24278

11367

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

27.633

24279

9828

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

27.634

24280

4400

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

27.635

24281

16680

\begin{align*} 2 x^{2} y^{\prime \prime }+5 y^{\prime } x +y&=85 \cos \left (2 \ln \left (x \right )\right ) \\ \end{align*}

27.666

24282

19296

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

27.674

24283

17047

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

27.679

24284

12068

\begin{align*} y^{\prime }&=\frac {y \ln \left (x \right )+\cosh \left (x \right ) x a y^{2}+\cosh \left (x \right ) x^{3} b}{x \ln \left (x \right )} \\ \end{align*}

27.685

24285

12066

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

27.688

24286

25032

\begin{align*} 3 y-5 t +2 y y^{\prime }-y^{\prime } t&=0 \\ \end{align*}

27.770

24287

26178

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

27.772

24288

20239

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

27.773

24289

23844

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

27.774

24290

13799

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

27.791

24291

12622

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

27.822

24292

17339

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

27.824

24293

4802

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

27.833

24294

11905

\begin{align*} y^{\prime }&=\frac {1}{y+2+\sqrt {1+3 x}} \\ \end{align*}

27.837

24295

17293

\begin{align*} 5 t +2 y+1+\left (2 t +y+1\right ) y^{\prime }&=0 \\ \end{align*}

27.867

24296

25444

\begin{align*} y^{\prime }&=2 y-{\mathrm e}^{i t} \\ \end{align*}

27.903

24297

16327

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

27.908

24298

1686

\begin{align*} -2 \sin \left (x \right ) y^{2}+3 y^{3}-2 x +\left (4 \cos \left (x \right ) y+9 x y^{2}\right ) y^{\prime }&=0 \\ \end{align*}

27.912

24299

21005

\begin{align*} x^{\prime }+\frac {\left (2 t^{3}+\sin \left (t \right )+5\right ) x}{t^{12}+5}&=0 \\ x \left (0\right ) &= 0 \\ \end{align*}

27.958

24300

5114

\begin{align*} \left (8+5 x -12 y\right ) y^{\prime }&=3+2 x -5 y \\ \end{align*}

27.978