2.4.24 first order ode reduced riccati

Table 2.1177: first order ode reduced riccati [68]

#

ODE

CAS classification

Solved

Maple

Mma

Sympy

time(sec)

40

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

[[_Riccati, _special]]

0.421

527

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

[[_Riccati, _special]]

6.339

528

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

[[_Riccati, _special]]

8.335

676

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

[_Riccati]

4.672

2348

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

[[_Riccati, _special]]

30.233

2358

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

[[_Riccati, _special]]

17.093

2523

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

[[_Riccati, _special]]

9.888

2533

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

[[_Riccati, _special]]

16.779

4652

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

[_Riccati]

8.440

4668

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

[[_Riccati, _special]]

30.832

4671

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

[[_Riccati, _special]]

36.770

4780

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

[_rational, [_Riccati, _special]]

6.516

4881

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

[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]]

7.020

4993

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

[_rational, [_Riccati, _special]]

8.767

5018

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

[_rational, [_Riccati, _special]]

0.310

7199

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

[_rational, _Riccati]

4.275

8268

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

[[_Riccati, _special]]

10.951

8289

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

[_Riccati]

8.598

8290

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

[_Riccati]

7.500

8292

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

[_Riccati]

6.140

8322

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

[[_Riccati, _special]]

7.417

10067

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

[[_Riccati, _special]]

6.247

10269

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

[[_Riccati, _special]]

29.630

10277

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

[[_Riccati, _special]]

28.050

10278

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

[[_Riccati, _special]]

4.136

10452

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

[[_Riccati, _special]]

4.655

11316

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

[[_Riccati, _special]]

29.387

11326

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

[[_Riccati, _special]]

29.213

11400

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

[_rational, [_Riccati, _special]]

2.783

11442

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

[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]]

4.205

11480

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

[_rational, [_Riccati, _special]]

5.105

13210

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

[[_Riccati, _special]]

33.462

13218

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

[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]]

5.169

13222

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

[_rational, [_Riccati, _special]]

5.822

14202

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

[[_Riccati, _special]]

14.314

14244

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

[[_Riccati, _special]]

8.874

15036

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

[[_Riccati, _special]]

34.610

15038

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

[_Riccati]

13.478

15042

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

[[_Riccati, _special]]

313.578

15532

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

[_Riccati]

12.984

15533

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

[_Riccati]

12.688

16201

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

[[_Riccati, _special]]

4.003

17034

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

[_Riccati]

8.862

17345

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

[[_Riccati, _special]]

22.181

17837

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

[[_Riccati, _special]]

12.220

17857

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

[_Riccati]

9.165

17871

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

[_Riccati]

9.558

17872

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

[[_Riccati, _special]]

280.695

19087

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

[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]]

3.444

19090

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

[_rational, [_Riccati, _special]]

4.039

19096

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

[_Riccati]

5.041

21028

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

[[_Riccati, _special]]

26.705

21048

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

[_Riccati]

9.850

21975

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

[[_Riccati, _special]]

8.059

23835

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

[[_Riccati, _special]]

9.046

24955

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

[[_Riccati, _special]]

9.967

25044

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

[[_Riccati, _special]]

274.027

25646

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

[[_Riccati, _special]]

8.634

25746

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

[[_Riccati, _special]]

17.770

25767

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

[_Riccati]

14.046

25768

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

[_Riccati]

13.003

25770

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

[_Riccati]

11.827

26174

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

[[_Riccati, _special]]

6.471

26190

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

[[_Riccati, _special]]

4.671

26206

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

[[_Riccati, _special]]

7.013

27257

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

[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]]

5.911

27291

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

[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]]

3.141

27335

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

[[_Riccati, _special]]

3.043