2.3.275 Problems 27401 to 27500

Table 2.1123: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

27401

13532

\begin{align*} y y^{\prime }-y&=A \,x^{2}-\frac {9}{625 A} \\ \end{align*}

115.965

27402

11296

\begin{align*} y^{\prime \prime }&=-\frac {\left (5 x^{2}+27\right ) y}{36 \left (x^{2}-1\right )^{2}} \\ \end{align*}

116.088

27403

20769

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

116.104

27404

13505

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

116.457

27405

3036

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

116.655

27406

20683

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

117.299

27407

18720

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

117.312

27408

23860

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

117.408

27409

11844

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

117.474

27410

5490

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

117.497

27411

5306

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

117.586

27412

23156

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

117.594

27413

5461

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

118.290

27414

11998

\begin{align*} y^{\prime }&=\frac {3 x^{4}+3 x^{3}+\sqrt {9 x^{4}-4 y^{3}}}{\left (x +1\right ) y^{2}} \\ \end{align*}

118.371

27415

10066

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

118.432

27416

13533

\begin{align*} y y^{\prime }-y&=-\frac {6}{25} x -A \,x^{2} \\ \end{align*}

118.737

27417

13820

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

118.751

27418

13447

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

118.924

27419

5568

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

119.327

27420

4581

\begin{align*} x_{1}^{\prime }&=-3 x_{1}+4 x_{2}-2 x_{3}+{\mathrm e}^{t} \\ x_{2}^{\prime }&=x_{1}+x_{2} \\ x_{3}^{\prime }&=6 x_{1}-6 x_{2}+5 x_{3} \\ \end{align*}

119.389

27421

26447

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

119.448

27422

13897

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

119.592

27423

12872

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

119.708

27424

13818

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

119.771

27425

20745

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

120.121

27426

20313

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

120.306

27427

18073

\begin{align*} \left (5 x -7 y+1\right ) y^{\prime }+x +y-1&=0 \\ \end{align*}

120.428

27428

7966

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

120.610

27429

26427

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

120.714

27430

13364

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

121.103

27431

13385

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

121.479

27432

20450

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

121.947

27433

17902

\begin{align*} x^{2} y^{\prime } \cos \left (y\right )+1&=0 \\ y \left (\infty \right ) &= \frac {16 \pi }{3} \\ \end{align*}

123.111

27434

13220

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

123.451

27435

20151

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

123.480

27436

18352

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

123.835

27437

20483

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

123.875

27438

13591

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

124.447

27439

11797

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

124.823

27440

20733

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

125.043

27441

20295

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

125.132

27442

18349

\begin{align*} x^{\prime \prime }+{\mathrm e}^{-x^{\prime }}-x&=0 \\ \end{align*}

127.523

27443

21958

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

127.533

27444

26412

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

127.659

27445

20952

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

128.517

27446

13480

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

129.507

27447

3018

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

129.655

27448

5566

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

129.685

27449

2778

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

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= -1 \\ x_{2} \left (0\right ) &= 0 \\ \end{align*}

129.733

27450

13534

\begin{align*} y y^{\prime }-y&=\frac {6}{25} x -A \,x^{2} \\ \end{align*}

129.924

27451

13497

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

130.455

27452

13374

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

130.616

27453

12950

\begin{align*} 2 y y^{\prime \prime }-{y^{\prime }}^{2}-8 y^{3}&=0 \\ \end{align*}

130.977

27454

13343

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

131.139

27455

4113

\begin{align*} 3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}

131.619

27456

17260

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

131.875

27457

22476

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

132.289

27458

22770

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

132.403

27459

16329

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

132.629

27460

13557

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

133.141

27461

20477

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

133.563

27462

27492

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

133.638

27463

5069

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

133.816

27464

13375

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

133.866

27465

12630

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

133.902

27466

13386

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

134.494

27467

5201

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

134.736

27468

26263

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

135.496

27469

5250

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

135.526

27470

13610

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

135.543

27471

13622

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

135.834

27472

12574

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

136.383

27473

11771

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

136.571

27474

12513

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

136.978

27475

13606

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

137.099

27476

13574

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

137.219

27477

21466

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

137.664

27478

16319

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

138.299

27479

5565

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

138.470

27480

13849

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

138.670

27481

12857

\begin{align*} y^{\prime \prime }+5 a y^{\prime }-6 y^{2}+6 a^{2} y&=0 \\ \end{align*}

138.983

27482

24155

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

139.168

27483

12581

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

140.422

27484

16325

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

141.036

27485

17291

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

141.342

27486

13879

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

141.715

27487

13815

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

141.829

27488

11619

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

142.071

27489

17322

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

142.134

27490

18732

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

142.413

27491

19783

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

142.660

27492

21982

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

142.749

27493

4986

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

142.762

27494

18341

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

143.861

27495

22397

\begin{align*} \left (3 x -y-9\right ) y^{\prime }&=10-2 x +2 y \\ \end{align*}

143.949

27496

6271

\begin{align*} \left (\operatorname {c2} \,x^{2}+\operatorname {b2} x +\operatorname {a2} \right ) y+\left (1-x \right ) x \left (\operatorname {b2} x +\operatorname {a1} \right ) y^{\prime }+\left (1-x \right )^{2} x^{2} y^{\prime \prime }&=0 \\ \end{align*}

144.101

27497

16191

\begin{align*} y^{\prime }&={\mathrm e}^{-9 x^{2}} \\ y \left (0\right ) &= 1 \\ \end{align*}

144.495

27498

20473

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

145.513

27499

13848

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

145.832

27500

13819

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

146.365