2.3.164 Problems 16301 to 16400

Table 2.901: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

16301

21026

\begin{align*} x^{\prime }+2 x&=6 t \\ \end{align*}

3.958

16302

1599

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

3.959

16303

6129

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

3.959

16304

6837

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

3.959

16305

18365

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

3.964

16306

27173

\begin{align*} x_{1}^{\prime }&=-2 x_{1}+x_{2} \\ x_{2}^{\prime }&=-4 x_{1}+3 x_{2}+10 \cos \left (t \right ) \\ \end{align*}

3.964

16307

2472

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

3.965

16308

3473

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

3.967

16309

23400

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

3.967

16310

19234

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

3.968

16311

15495

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

3.969

16312

3518

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

3.970

16313

4691

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

3.970

16314

14971

\begin{align*} 3 x^{2} z^{\prime \prime }+5 x z^{\prime }-z&=0 \\ z \left (1\right ) &= 2 \\ z^{\prime }\left (1\right ) &= -1 \\ \end{align*}

3.970

16315

93

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

3.971

16316

5075

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

3.971

16317

5976

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

3.971

16318

5942

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

3.972

16319

24670

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

3.972

16320

8327

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

3.973

16321

12537

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

3.973

16322

16628

\begin{align*} y^{\prime \prime }+4 y^{\prime }&=20 \\ \end{align*}

3.973

16323

17066

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

3.973

16324

6508

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

3.974

16325

9210

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

3.974

16326

19483

\begin{align*} x^{2} y^{\prime \prime }+3 y^{\prime } x +10 y&=0 \\ \end{align*}

3.976

16327

6063

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

3.977

16328

12556

\begin{align*} 50 x \left (-1+x \right ) y^{\prime \prime }+25 \left (2 x -1\right ) y^{\prime }-2 y&=0 \\ \end{align*}

3.977

16329

11353

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

3.978

16330

27040

\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=8 \delta \left (t \right ) \\ y \left (0\right ) &= 3 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

3.979

16331

12186

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

3.980

16332

21619

\begin{align*} m y^{\prime \prime }+a y^{\prime }+k y&=0 \\ \end{align*}

3.980

16333

6018

\begin{align*} \operatorname {a2} y+\operatorname {a1} x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}

3.981

16334

24571

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

3.981

16335

12289

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

3.983

16336

7351

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

3.984

16337

17006

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

3.984

16338

17246

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

3.984

16339

1523

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

3.985

16340

16390

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

3.985

16341

17344

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

3.986

16342

16734

\begin{align*} 2 y^{\prime \prime }-7 y^{\prime }+3&=0 \\ \end{align*}

3.987

16343

26446

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

3.987

16344

4812

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

3.990

16345

15320

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

3.990

16346

4301

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

3.991

16347

18838

\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&={\mathrm e}^{t} \cos \left (2 t \right )+{\mathrm e}^{2 t} \left (3 t +4\right ) \sin \left (t \right ) \\ \end{align*}

3.992

16348

7728

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

3.993

16349

3408

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

3.994

16350

5001

\begin{align*} x^{5} y^{\prime }&=1-3 x^{4} y \\ \end{align*}

3.994

16351

10179

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

Series expansion around \(x=0\).

3.994

16352

4323

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

3.997

16353

13041

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

3.997

16354

17325

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

3.997

16355

3477

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

3.999

16356

5384

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

3.999

16357

749

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

4.000

16358

3384

\begin{align*} x^{2} y^{\prime \prime }+x \left (x -7\right ) y^{\prime }+\left (x +12\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

4.000

16359

7595

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

4.000

16360

19285

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

4.001

16361

19489

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

4.001

16362

7428

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

4.002

16363

14902

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

4.003

16364

15242

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

Using Laplace transform method.

4.003

16365

19790

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

4.003

16366

5013

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

4.004

16367

42

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

4.006

16368

4715

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

4.006

16369

9744

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

4.006

16370

19322

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

4.006

16371

5223

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

4.007

16372

5509

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

4.007

16373

19332

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

4.007

16374

1166

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

4.008

16375

18519

\begin{align*} -y+y^{\prime } t&=t^{3} {\mathrm e}^{-t} \\ \end{align*}

4.009

16376

4761

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

4.010

16377

6499

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

4.010

16378

4736

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

4.012

16379

7009

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

4.012

16380

21951

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

4.012

16381

5219

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

4.013

16382

2990

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

4.014

16383

6974

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

4.016

16384

17334

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

4.016

16385

21950

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

4.016

16386

4839

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

4.017

16387

4349

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

4.019

16388

8335

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

4.019

16389

1138

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

4.020

16390

4981

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

4.020

16391

9277

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

4.020

16392

12032

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

4.020

16393

18489

\begin{align*} y^{\prime }&=\frac {3 x}{y+x^{2} y} \\ y \left (0\right ) &= -7 \\ \end{align*}

4.020

16394

4647

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

4.022

16395

5451

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

4.024

16396

3597

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

4.026

16397

673

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

4.027

16398

5448

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

4.027

16399

1129

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

4.028

16400

6977

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

4.028