2.3.170 Problems 16901 to 17000

Table 2.871: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

16901

19748

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

4.327

16902

2566

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=0 \\ \end{align*}

4.328

16903

12936

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

4.328

16904

1554

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

4.329

16905

1570

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

4.329

16906

8880

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

4.329

16907

7676

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

4.332

16908

25217

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

4.332

16909

11515

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

4.333

16910

11825

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

4.333

16911

17664

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

4.333

16912

18760

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

4.333

16913

15414

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

4.334

16914

17933

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

4.334

16915

14211

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

4.335

16916

23851

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

4.335

16917

17015

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

4.336

16918

20641

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

4.336

16919

21956

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

4.339

16920

674

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

4.340

16921

18148

\begin{align*} y^{\prime \prime }-7 y^{\prime }&=\left (x -1\right )^{2} \\ \end{align*}

4.340

16922

10163

\begin{align*} v v^{\prime }&=\frac {2 v^{2}}{r^{3}}+\frac {\lambda r}{3} \\ \end{align*}

4.341

16923

18763

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

4.341

16924

2551

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

4.343

16925

4118

\begin{align*} y^{\prime \prime }+2 y^{\prime }-15 y&=0 \\ \end{align*}

4.343

16926

6020

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

4.345

16927

9143

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

4.346

16928

20498

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

4.346

16929

21976

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

4.347

16930

25497

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

4.347

16931

24472

\begin{align*} y^{\prime \prime }-9 y&=0 \\ \end{align*}

4.348

16932

19745

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

4.352

16933

24187

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

4.352

16934

1276

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

4.353

16935

4210

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

4.353

16936

8892

\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&=0 \\ \end{align*}

4.353

16937

25207

\begin{align*} t^{2} y^{\prime \prime }-4 y^{\prime } t +6 y&=t^{5} \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= 1 \\ \end{align*}

4.353

16938

1148

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

4.355

16939

15174

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

4.356

16940

22389

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

4.356

16941

902

\begin{align*} x^{2} y^{\prime \prime }+y^{\prime } x -y&=72 x^{5} \\ \end{align*}

4.357

16942

19631

\begin{align*} y^{\prime \prime }+x^{2} y&=0 \\ y \left (0\right ) &= y_{0} \\ y^{\prime }\left (0\right ) &= \operatorname {yd}_{0} \\ \end{align*}
Using Laplace transform method.

4.357

16943

12337

\begin{align*} y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}}&=0 \\ \end{align*}

4.358

16944

14584

\begin{align*} y^{\prime \prime }+9 y&=0 \\ \end{align*}

4.358

16945

737

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

4.359

16946

1204

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

4.360

16947

4943

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

4.360

16948

25195

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

4.361

16949

714

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

4.362

16950

4799

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

4.362

16951

7567

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

4.362

16952

21171

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

4.362

16953

24217

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

4.362

16954

2374

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

4.364

16955

7371

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

4.364

16956

14279

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

4.364

16957

17020

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

4.364

16958

2986

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

4.365

16959

7513

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

4.366

16960

7262

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

4.367

16961

17981

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

4.368

16962

22709

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

4.368

16963

25031

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

4.368

16964

4780

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

4.369

16965

4121

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

4.370

16966

2532

\begin{align*} y^{\prime }&=\frac {\left (1+\cos \left (4 t \right )\right ) y}{4}-\frac {\left (1-\cos \left (4 t \right )\right ) y^{2}}{800} \\ y \left (0\right ) &= 100 \\ \end{align*}

4.372

16967

17535

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

4.372

16968

20330

\begin{align*} 2 x^{\prime \prime }+5 x^{\prime }-12 x&=0 \\ \end{align*}

4.372

16969

23399

\begin{align*} 3 y^{\prime \prime } x -4 y^{\prime }+\frac {5 y}{x}&=0 \\ \end{align*}

4.372

16970

1354

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

4.373

16971

12045

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

4.373

16972

3217

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

4.375

16973

744

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

4.376

16974

16253

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

4.376

16975

25540

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

4.378

16976

5041

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

4.379

16977

1309

\begin{align*} 4 y^{\prime \prime }+17 y^{\prime }+4 y&=0 \\ \end{align*}

4.380

16978

1824

\begin{align*} 4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}+3\right ) y&=x^{{7}/{2}} \\ \end{align*}

4.381

16979

7683

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

4.381

16980

6179

\begin{align*} -\left (5+4 x \right ) y+32 y^{\prime } x +16 x^{2} y^{\prime \prime }&=0 \\ \end{align*}

4.382

16981

17313

\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{8 y}}{t} \\ \end{align*}

4.382

16982

8382

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

4.383

16983

5754

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

4.384

16984

15941

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

4.385

16985

17148

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

4.385

16986

1849

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

4.386

16987

20605

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

4.386

16988

21611

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

4.386

16989

19087

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

4.387

16990

3603

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

4.389

16991

22446

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

4.390

16992

8372

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

4.391

16993

14036

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

4.391

16994

20098

\begin{align*} x^{2} y^{\prime \prime }+2 y^{\prime } x -20 y&=\left (x +1\right )^{2} \\ \end{align*}

4.391

16995

8303

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

4.393

16996

11614

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

4.393

16997

13639

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

4.393

16998

19672

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

4.394

16999

19969

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

4.394

17000

6063

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

4.395