2.3.222 Problems 22101 to 22200

Table 2.993: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

22101

3674

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

8.445

22102

4530

\begin{align*} y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-4 y&=40 \operatorname {Heaviside}\left (-2+t \right ) t^{2} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

8.452

22103

18814

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

8.453

22104

4426

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

8.456

22105

4764

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

8.460

22106

12327

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

8.460

22107

21929

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

8.460

22108

4808

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

8.467

22109

23020

\begin{align*} z^{\prime \prime }+g z&=0 \\ z \left (\frac {\pi }{3 \sqrt {g}}\right ) &= 5 \\ z \left (\frac {2 \pi }{3 \sqrt {g}}\right ) &= \frac {\pi }{3} \\ \end{align*}

8.470

22110

11937

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

8.471

22111

7694

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

8.473

22112

214

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

8.474

22113

25870

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

8.479

22114

25004

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

8.480

22115

1608

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

8.483

22116

4790

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

8.486

22117

24230

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

8.487

22118

11691

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

8.497

22119

17885

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

8.497

22120

4823

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

8.498

22121

7033

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

8.504

22122

12205

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

8.504

22123

19897

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

8.504

22124

18935

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

8.510

22125

21075

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

8.511

22126

18849

\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=\left \{\begin {array}{cc} 1 & 0\le t \le \frac {\pi }{2} \\ 0 & \frac {\pi }{2}<t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

8.513

22127

21787

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

8.513

22128

24193

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

8.516

22129

24350

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

8.529

22130

13906

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

8.535

22131

19098

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

8.535

22132

12157

\begin{align*} y^{\prime }&=\frac {-2 y x +2 x^{3}-2 x -y^{3}+3 y^{2} x^{2}-3 x^{4} y+x^{6}}{-y+x^{2}-1} \\ \end{align*}

8.539

22133

15620

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

8.550

22134

22536

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

8.550

22135

13718

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

8.551

22136

4333

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

8.552

22137

11335

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

8.558

22138

12365

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

8.560

22139

15541

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

8.562

22140

7534

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

8.566

22141

6425

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

8.570

22142

13962

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

8.572

22143

6806

\begin{align*} {y^{\prime }}^{3} y^{\prime \prime \prime }&=1 \\ \end{align*}

8.574

22144

26280

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

8.574

22145

13369

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

8.575

22146

5272

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

8.576

22147

17928

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

8.588

22148

12323

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

8.598

22149

13492

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

8.598

22150

7607

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

8.603

22151

6538

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

8.606

22152

24190

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

8.606

22153

14907

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

8.611

22154

5705

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

8.614

22155

25885

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

8.617

22156

19767

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

8.621

22157

21058

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

8.622

22158

23150

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

8.624

22159

17671

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

8.625

22160

18072

\begin{align*} y^{\prime }&=\sqrt {\frac {9 y^{2}-6 y+2}{x^{2}-2 x +5}} \\ \end{align*}

8.625

22161

12161

\begin{align*} y^{\prime }&=\frac {-18 y x -6 x^{3}-18 x +27 y^{3}+27 y^{2} x^{2}+9 x^{4} y+x^{6}}{27 y+9 x^{2}+27} \\ \end{align*}

8.626

22162

12194

\begin{align*} y^{\prime }&=\frac {2 a \left (x y^{2}-4 a +x \right )}{-x^{3} y^{3}+4 a \,x^{2} y-x^{3} y+2 a y^{6} x^{3}-24 y^{4} a^{2} x^{2}+96 y^{2} x \,a^{3}-128 a^{4}} \\ \end{align*}

8.632

22163

5160

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

8.640

22164

5709

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

8.642

22165

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*}

8.648

22166

6572

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

8.649

22167

7400

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

8.652

22168

9336

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

8.652

22169

21338

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

8.655

22170

12330

\begin{align*} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+\left (\operatorname {a1} \,x^{2}+\operatorname {b1} x +\operatorname {c1} \right ) y&=0 \\ \end{align*}

8.663

22171

11588

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

8.664

22172

12140

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

8.667

22173

12379

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

8.669

22174

12178

\begin{align*} y^{\prime }&=\frac {32 y x^{5}+8 x^{3}+32 x^{5}+64 x^{6} y^{3}+48 y^{2} x^{4}+12 x^{2} y+1}{16 x^{6} \left (4 x^{2} y+1+4 x^{2}\right )} \\ \end{align*}

8.674

22175

14079

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

8.677

22176

5025

\begin{align*} y^{\prime } \sqrt {a_{4} x^{4}+a_{3} x^{3}+a_{2} x^{2}+a_{1} x +a_{0}}&=\sqrt {b_{0} +b_{1} y+b_{2} y^{2}} \\ \end{align*}

8.678

22177

11920

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

8.679

22178

6415

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

8.682

22179

19383

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

8.682

22180

4529

\begin{align*} y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y&=120 \,{\mathrm e}^{3 t} \operatorname {Heaviside}\left (t -1\right ) \\ y \left (0\right ) &= 15 \\ y^{\prime }\left (0\right ) &= -6 \\ y^{\prime \prime }\left (0\right ) &= 0 \\ y^{\prime \prime \prime }\left (0\right ) &= 0 \\ \end{align*}
Using Laplace transform method.

8.683

22181

9789

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

8.687

22182

26289

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

8.688

22183

4524

\begin{align*} y^{\prime \prime }+4 y&=8 \left (t^{2}+t -1\right ) \operatorname {Heaviside}\left (-2+t \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}
Using Laplace transform method.

8.694

22184

12201

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

8.695

22185

24832

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

8.698

22186

19310

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

8.700

22187

20751

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

8.707

22188

12397

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

8.710

22189

12033

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

8.719

22190

3277

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

8.720

22191

22385

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

8.723

22192

25008

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

8.723

22193

24329

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

8.724

22194

26294

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

8.727

22195

7693

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

8.732

22196

8236

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

8.732

22197

9492

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

8.734

22198

22435

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

8.736

22199

13216

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

8.741

22200

13971

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

8.744