2.3.239 Problems 23801 to 23900

Table 2.1051: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

23801

25842

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

10.964

23802

3668

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

10.967

23803

4359

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

10.968

23804

18507

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

10.971

23805

4298

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

10.980

23806

21184

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

10.998

23807

7493

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

11.010

23808

15056

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

11.015

23809

22953

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

11.020

23810

25889

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

11.030

23811

12083

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

11.031

23812

15448

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

11.035

23813

5610

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

11.040

23814

18621

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

11.043

23815

4840

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

11.050

23816

22984

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

11.053

23817

24312

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

11.054

23818

13711

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

11.062

23819

3677

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

11.063

23820

5028

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

11.064

23821

2883

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

11.066

23822

8234

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

11.066

23823

14436

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

11.070

23824

4399

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

11.072

23825

11578

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

11.072

23826

3657

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

11.079

23827

25826

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

11.081

23828

24887

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

11.084

23829

16679

\begin{align*} 2 x^{2} y^{\prime \prime }-x y^{\prime }+y&=\frac {50}{x^{3}} \\ \end{align*}

11.088

23830

26913

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

11.090

23831

4826

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

11.093

23832

15063

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

11.098

23833

10134

\begin{align*} w^{\prime }&=-\frac {1}{2}-\frac {\sqrt {1-12 w}}{2} \\ w \left (1\right ) &= -1 \\ \end{align*}

11.108

23834

761

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

11.119

23835

4726

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

11.130

23836

11799

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

11.135

23837

14519

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

11.136

23838

23287

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

11.137

23839

8801

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

11.147

23840

6999

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

11.151

23841

9164

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

11.153

23842

12101

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

11.155

23843

15344

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

11.155

23844

5126

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

11.169

23845

3307

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

11.171

23846

15043

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

11.173

23847

23217

\begin{align*} y^{\prime }&=\frac {5 x -y-2}{x +y+4} \\ \end{align*}

11.174

23848

11562

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

11.178

23849

9997

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

11.180

23850

1710

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

11.181

23851

25837

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

11.188

23852

6346

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

11.190

23853

11971

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

11.190

23854

13394

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

11.190

23855

14471

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

11.194

23856

14240

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

11.196

23857

25865

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

11.199

23858

21085

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

11.208

23859

21965

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

11.209

23860

2869

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

11.210

23861

733

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

11.213

23862

6562

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

11.214

23863

24203

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

11.218

23864

5195

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

11.227

23865

7401

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

11.228

23866

6349

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

11.232

23867

3661

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

11.237

23868

22409

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

11.243

23869

13712

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

11.245

23870

20259

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

11.245

23871

13690

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

11.246

23872

4873

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

11.255

23873

24208

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

11.261

23874

27435

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

11.262

23875

17957

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

11.263

23876

14236

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

11.272

23877

6818

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

11.273

23878

13465

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

11.276

23879

12043

\begin{align*} y^{\prime }&=\frac {-4 y x -x^{3}+4 x^{2}-4 x +8}{8 y+2 x^{2}-8 x +8} \\ \end{align*}

11.279

23880

14277

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

11.280

23881

5103

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

11.281

23882

11587

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

11.296

23883

13442

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

11.296

23884

3681

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

11.300

23885

3225

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

11.305

23886

6844

\begin{align*} z^{\prime }+2 x z&=2 a \,x^{3} z^{3} \\ \end{align*}

11.305

23887

15894

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

11.307

23888

19235

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

11.309

23889

6426

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

11.315

23890

3288

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

11.325

23891

17174

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

11.326

23892

3229

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

11.332

23893

18110

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

11.332

23894

19804

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

11.336

23895

14357

\begin{align*} x^{\prime \prime }+\frac {2 x^{\prime }}{5}+2 x&=1-\operatorname {Heaviside}\left (t -5\right ) \\ x \left (0\right ) &= 0 \\ x^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

11.339

23896

5039

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

11.342

23897

19964

\begin{align*} 3 y+2 x +4-\left (4 x +6 y+5\right ) y^{\prime }&=0 \\ \end{align*}

11.342

23898

5428

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

11.352

23899

12243

\begin{align*} y^{\prime }&=\frac {-4 x \cos \left (x \right )+4 x^{2} \sin \left (x \right )+4 x +4+4 y^{2}+8 y \cos \left (x \right ) x -8 y x +2 x^{2} \cos \left (2 x \right )+6 x^{2}-8 x^{2} \cos \left (x \right )+4 y^{3}+12 y^{2} \cos \left (x \right ) x -12 x y^{2}+6 y x^{2} \cos \left (2 x \right )+18 x^{2} y-24 y \cos \left (x \right ) x^{2}+x^{3} \cos \left (3 x \right )+15 x^{3} \cos \left (x \right )-6 x^{3} \cos \left (2 x \right )-10 x^{3}}{4 x} \\ \end{align*}

11.360

23900

3773

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

11.364