2.3.222 Problems 22101 to 22200

Table 2.1017: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

22101

18077

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

6.677

22102

22368

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

6.680

22103

12175

\begin{align*} y^{\prime }&=\frac {\left (-256 a \,x^{2} y-32 a^{2} x^{6}-256 a \,x^{2}+512 y^{3}+192 x^{4} a y^{2}+24 y a^{2} x^{8}+a^{3} x^{12}\right ) x}{512 y+64 a \,x^{4}+512} \\ \end{align*}

6.681

22104

14233

\begin{align*} x^{\prime }&=\frac {\left (4+2 t \right ) x}{\ln \left (x\right )} \\ x \left (0\right ) &= {\mathrm e} \\ \end{align*}

6.681

22105

111

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

6.684

22106

7929

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

6.685

22107

4285

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

6.687

22108

20548

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

6.688

22109

19094

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

6.691

22110

20324

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

6.691

22111

21873

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

6.691

22112

735

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

6.692

22113

11488

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

6.694

22114

18516

\begin{align*} 2 y t +y^{\prime }&=16 t \,{\mathrm e}^{-t^{2}} \\ \end{align*}

6.694

22115

2905

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

6.699

22116

20238

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

6.701

22117

8689

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

6.703

22118

4858

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

6.704

22119

24390

\begin{align*} 5 x +3 \,{\mathrm e}^{y}+2 x \,{\mathrm e}^{y} y^{\prime }&=0 \\ \end{align*}

6.704

22120

27414

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

6.706

22121

8025

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

6.708

22122

23869

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

6.710

22123

11386

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

6.713

22124

13233

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

6.713

22125

15489

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

6.713

22126

17971

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

6.714

22127

24252

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

6.717

22128

17879

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

6.719

22129

11691

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

6.720

22130

6878

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

6.723

22131

20217

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

6.723

22132

18533

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

6.724

22133

8670

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

6.725

22134

18056

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

6.727

22135

20575

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

6.729

22136

6150

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

6.731

22137

19859

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

6.732

22138

7350

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

6.733

22139

13318

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

6.736

22140

21845

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

6.737

22141

22487

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

6.737

22142

5604

\begin{align*} 3 x y^{4} {y^{\prime }}^{2}-y^{5} y^{\prime }+1&=0 \\ \end{align*}

6.739

22143

14929

\begin{align*} y^{\prime \prime }-4 y&=0 \\ y \left (0\right ) &= 10 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

6.740

22144

18377

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

Series expansion around \(x={\mathrm e}\).

6.742

22145

9198

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

6.743

22146

26237

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

6.744

22147

26902

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

6.744

22148

1626

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

6.746

22149

5136

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

6.747

22150

7030

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

6.747

22151

21436

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

6.748

22152

22450

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

6.748

22153

1695

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

6.749

22154

4657

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

6.749

22155

3431

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

6.750

22156

26224

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

6.751

22157

9538

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

Series expansion around \(x=0\).

6.752

22158

6545

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

6.753

22159

6966

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

6.754

22160

4704

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

6.759

22161

19109

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

6.759

22162

6058

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

6.760

22163

4822

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

6.762

22164

9928

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

Series expansion around \(x=0\).

6.762

22165

13682

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

6.762

22166

22355

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

6.764

22167

9040

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

6.766

22168

12085

\begin{align*} y^{\prime }&=\frac {\textit {\_F1} \left (y^{2}-2 \ln \left (x \right )\right )}{\sqrt {y^{2}}\, x} \\ \end{align*}

6.769

22169

22506

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

6.769

22170

13993

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

6.770

22171

19133

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

6.770

22172

2512

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

6.771

22173

1598

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

6.773

22174

2357

\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*}

6.773

22175

20266

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

6.773

22176

4729

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

6.777

22177

19815

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

6.783

22178

21445

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

6.783

22179

11724

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

6.784

22180

5138

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

6.785

22181

17310

\begin{align*} y^{\prime }&=\frac {2 t^{5}}{5 y^{2}} \\ \end{align*}

6.786

22182

14524

\begin{align*} 8 x^{3} y-12 x^{3}+\left (x^{4}+1\right ) y^{\prime }&=0 \\ \end{align*}

6.787

22183

15606

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

6.789

22184

21064

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

6.789

22185

11383

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

6.791

22186

12688

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

6.793

22187

2974

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

6.794

22188

27512

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

6.794

22189

6056

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

6.795

22190

8828

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

6.796

22191

10323

\begin{align*} y^{\prime }&=\left (a +b x +c y\right )^{6} \\ \end{align*}

6.796

22192

11986

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

6.798

22193

24204

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

6.798

22194

2957

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

6.799

22195

3456

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

6.801

22196

27355

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

6.802

22197

3656

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

6.803

22198

11925

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

6.803

22199

15326

\begin{align*} c v^{\prime \prime }+\frac {v^{\prime }}{r}+\frac {v}{L}&=\delta \left (t -1\right )-\delta \left (t \right ) \\ \end{align*}

Using Laplace transform method.

6.803

22200

24144

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

6.803