2.3.259 Problems 25801 to 25900

Table 2.1091: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

25801

11642

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

27.825

25802

2894

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

27.839

25803

15170

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

27.840

25804

25716

\begin{align*} y^{\prime }&=\sqrt {y^{2}-9} \\ y \left (5\right ) &= 3 \\ \end{align*}

27.882

25805

24407

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

27.888

25806

13253

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

27.891

25807

9167

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

27.908

25808

21922

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

27.915

25809

24343

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

27.915

25810

2879

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

27.920

25811

17085

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

27.938

25812

12386

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

27.939

25813

13792

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

27.955

25814

18535

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

27.957

25815

11629

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

27.958

25816

5228

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

27.965

25817

17231

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

27.999

25818

3478

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

28.006

25819

5177

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

28.010

25820

22064

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

28.013

25821

23879

\begin{align*} y^{\prime }&=\frac {4 x -3 y-17}{3 x +y-3} \\ \end{align*}

28.036

25822

10277

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

28.050

25823

2963

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

28.053

25824

8712

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

28.088

25825

21328

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

28.095

25826

11605

\begin{align*} \left (3 x^{3}+6 x^{2} y-3 x y^{2}+20 y^{3}\right ) y^{\prime }+4 x^{3}+9 x^{2} y+6 x y^{2}-y^{3}&=0 \\ \end{align*}

28.096

25827

24234

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

28.105

25828

17304

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

28.129

25829

22536

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

28.161

25830

21421

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

28.189

25831

11556

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

28.196

25832

21378

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

28.211

25833

2873

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

28.216

25834

24408

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

28.235

25835

13267

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

28.248

25836

11513

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

28.249

25837

4280

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

28.250

25838

17320

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

28.254

25839

4289

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

28.266

25840

19720

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

28.292

25841

17972

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

28.299

25842

3055

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

28.303

25843

27456

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

28.305

25844

5146

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

28.326

25845

26296

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

28.355

25846

22433

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

28.361

25847

15509

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

28.382

25848

11793

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

28.383

25849

7248

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

28.418

25850

25443

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

28.419

25851

14453

\begin{align*} \frac {1+8 x y^{{2}/{3}}}{x^{{2}/{3}} y^{{1}/{3}}}+\frac {\left (2 x^{{4}/{3}} y^{{2}/{3}}-x^{{1}/{3}}\right ) y^{\prime }}{y^{{4}/{3}}}&=0 \\ y \left (1\right ) &= 8 \\ \end{align*}

28.430

25852

22756

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

28.430

25853

13994

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

28.431

25854

24287

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

28.444

25855

9131

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

28.457

25856

4877

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

28.460

25857

13808

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

28.470

25858

23903

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

28.483

25859

5233

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

28.484

25860

21279

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

28.497

25861

2350

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

28.523

25862

5551

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

28.529

25863

11399

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

28.564

25864

20435

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

28.566

25865

21811

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

28.576

25866

24394

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

28.596

25867

14275

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

28.617

25868

5256

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

28.632

25869

25878

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

28.638

25870

2351

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

28.663

25871

22426

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

28.680

25872

22293

\begin{align*} r^{\prime }&=\sqrt {r t} \\ \end{align*}

28.721

25873

19709

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

28.725

25874

18934

\begin{align*} u^{\prime \prime }+\frac {u^{\prime }}{4}+u&=\frac {\left (\left \{\begin {array}{cc} 1 & \frac {3}{2}\le t <\frac {5}{2} \\ 0 & \operatorname {otherwise} \end {array}\right .\right )}{2} \\ u \left (0\right ) &= 0 \\ u^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

28.734

25875

16362

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

28.738

25876

12568

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

28.790

25877

20314

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

28.800

25878

20681

\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*}

28.813

25879

11801

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

28.815

25880

12082

\begin{align*} y^{\prime }&=\frac {-b^{3}+6 b^{2} x -12 b \,x^{2}+8 x^{3}-4 b y^{2}+8 x y^{2}+8 y^{3}}{\left (2 x -b \right )^{3}} \\ \end{align*}

28.817

25881

5055

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

28.849

25882

13553

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

28.864

25883

24194

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

28.871

25884

11451

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

28.882

25885

4850

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

28.911

25886

4330

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

28.941

25887

2893

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

28.958

25888

3546

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

29.000

25889

8310

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

29.060

25890

25902

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

29.077

25891

18287

\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=2 \,{\mathrm e}^{x} \left (\sin \left (x \right )+7 \cos \left (x \right )\right ) \\ y \left (-\infty \right ) &= 0 \\ \end{align*}

29.085

25892

22403

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

29.094

25893

5017

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

29.101

25894

23294

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

29.102

25895

11846

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

29.124

25896

6023

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

29.133

25897

5052

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

29.144

25898

24331

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

29.153

25899

8673

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

29.169

25900

11814

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

29.176