2.3.236 Problems 23501 to 23600

Table 2.1045: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

23501

19823

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

10.010

23502

12073

\begin{align*} y^{\prime }&=\frac {2 x^{2} \cosh \left (\frac {1}{x -1}\right )-2 x \cosh \left (\frac {1}{x -1}\right )-1+y^{2}-2 x^{2} y+x^{4}-x +x y^{2}-2 x^{3} y+x^{5}}{\left (x -1\right ) \cosh \left (\frac {1}{x -1}\right )} \\ \end{align*}

10.013

23503

12227

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

10.013

23504

1198

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

10.022

23505

24942

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

10.025

23506

25724

\begin{align*} y^{\prime \prime }+9 y&=0 \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (\frac {\pi }{6}\right ) &= -1 \\ \end{align*}

10.025

23507

4783

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

10.031

23508

16476

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

10.031

23509

5354

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

10.034

23510

7867

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

10.036

23511

11532

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

10.039

23512

8402

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

10.043

23513

24213

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

10.044

23514

19072

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

10.053

23515

14533

\begin{align*} 8+2 y^{2}+\left (-x^{2}+1\right ) y y^{\prime }&=0 \\ y \left (3\right ) &= 0 \\ \end{align*}

10.054

23516

15336

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

10.058

23517

18545

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

10.059

23518

2931

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

10.060

23519

20502

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

10.061

23520

6048

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

10.079

23521

16297

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

10.084

23522

22063

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

10.085

23523

8243

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

10.086

23524

22373

\begin{align*} r^{\prime }&=\frac {\sin \left (t \right )+{\mathrm e}^{r} \sin \left (t \right )}{3 \,{\mathrm e}^{r}+{\mathrm e}^{r} \cos \left (2 t \right )} \\ r \left (\frac {\pi }{2}\right ) &= 0 \\ \end{align*}

10.088

23525

23844

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

10.096

23526

12042

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

10.099

23527

22562

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

10.099

23528

2690

\begin{align*} y^{\prime \prime }+y^{\prime }+7 y&=\left \{\begin {array}{cc} t & 0\le t <2 \\ 0 & 2\le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

10.104

23529

19277

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

10.105

23530

18563

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

10.116

23531

4690

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

10.120

23532

9152

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

10.120

23533

4793

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

10.126

23534

10114

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

10.127

23535

21054

\begin{align*} x^{\prime }&=4 t^{3} x^{4} \\ \end{align*}

10.135

23536

12942

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

10.145

23537

17925

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

10.145

23538

4315

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

10.148

23539

12131

\begin{align*} y^{\prime }&=\frac {1}{\sin \left (x \right )}+\textit {\_F1} \left (y-\ln \left (\sin \left (x \right )\right )+\ln \left (1+\cos \left (x \right )\right )\right ) \\ \end{align*}

10.151

23540

11487

\begin{align*} x^{1+2 n} y^{\prime }-a y^{3}-b \,x^{3 n}&=0 \\ \end{align*}

10.158

23541

17874

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

10.158

23542

12229

\begin{align*} y^{\prime }&=\frac {x^{2} y+x^{4}+2 x^{3}-3 x^{2}+y x +x +y^{3}+3 x^{2} y^{2}-3 x y^{2}+3 x^{4} y-6 x^{3} y+x^{6}-3 x^{5}}{x \left (y+x^{2}-x +1\right )} \\ \end{align*}

10.162

23543

5844

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

10.168

23544

3025

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

10.171

23545

1608

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

10.178

23546

13365

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

10.179

23547

5856

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

10.184

23548

22774

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

10.193

23549

11371

\begin{align*} y^{\prime }-\sqrt {\frac {a_{4} x^{4}+a_{3} x^{3}+a_{2} x^{2}+a_{1} x +a_{0}}{b_{4} y^{4}+b_{3} y^{3}+b_{2} y^{2}+b_{1} y+b_{0}}}&=0 \\ \end{align*}

10.199

23550

22555

\begin{align*} q^{\prime }&=\frac {p \,{\mathrm e}^{p^{2}-q^{2}}}{q} \\ \end{align*}

10.206

23551

26330

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

10.207

23552

17947

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

10.211

23553

11598

\begin{align*} \left (10 x^{3} y^{2}+x^{2} y+2 x \right ) y^{\prime }+5 x^{2} y^{3}+x y^{2}&=0 \\ \end{align*}

10.212

23554

7744

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

10.213

23555

11654

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

10.215

23556

27209

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

10.222

23557

24384

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

10.227

23558

12099

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

10.228

23559

14039

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

10.235

23560

13706

\begin{align*} y^{\prime \prime }+a \,x^{n} y^{\prime }+b \,x^{n -1} y&=0 \\ \end{align*}

10.242

23561

11461

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

10.246

23562

5156

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

10.252

23563

11546

\begin{align*} \left (a x y+b \,x^{n}\right ) y^{\prime }+\alpha y^{3}+\beta y^{2}&=0 \\ \end{align*}

10.255

23564

4862

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

10.257

23565

20589

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

10.258

23566

14235

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

10.259

23567

13329

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

10.261

23568

15323

\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=\left \{\begin {array}{cc} t & 0\le t \le 3 \\ t +2 & 3<t \end {array}\right . \\ y \left (0\right ) &= -2 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

Using Laplace transform method.

10.265

23569

6568

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

10.267

23570

22505

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

10.281

23571

10311

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

10.283

23572

22988

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

10.290

23573

12262

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

10.291

23574

16350

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

10.295

23575

4875

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

10.296

23576

22954

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

10.296

23577

20232

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

10.300

23578

3029

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

10.303

23579

4328

\begin{align*} 3 \left (x^{2}-1\right ) y+\left (x^{3}+8 y-3 x \right ) y^{\prime }&=0 \\ \end{align*}

10.303

23580

13760

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

10.309

23581

20250

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

10.309

23582

9137

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

10.314

23583

25015

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

10.315

23584

27387

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

10.316

23585

4692

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

10.317

23586

14895

\begin{align*} m v^{\prime }&=-m g +k v^{2} \\ \end{align*}

10.318

23587

5679

\begin{align*} {y^{\prime }}^{6}+f \left (x \right ) \left (y-a \right )^{5} \left (y-b \right )^{3}&=0 \\ \end{align*}

10.320

23588

9492

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

10.323

23589

27409

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

10.323

23590

4889

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

10.326

23591

23248

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

10.328

23592

732

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

10.330

23593

8700

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

10.335

23594

15380

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

10.337

23595

19321

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

10.341

23596

135

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

10.343

23597

163

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

10.345

23598

5175

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

10.345

23599

19706

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

10.345

23600

21926

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

10.346