2.3.232 Problems 23101 to 23200

Table 2.1037: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

23101

22437

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

19.095

23102

13226

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

19.098

23103

740

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

19.106

23104

25464

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

19.108

23105

15038

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

19.113

23106

21089

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

19.129

23107

2896

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

19.145

23108

21030

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

19.155

23109

5261

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

19.156

23110

16304

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

19.158

23111

5593

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

19.163

23112

9597

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

Series expansion around \(x=0\).

19.164

23113

14461

\begin{align*} \tan \left (\theta \right )+2 r \theta ^{\prime }&=0 \\ \end{align*}

19.171

23114

25691

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

19.171

23115

5160

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

19.174

23116

7562

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

19.193

23117

24836

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

19.194

23118

4260

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

19.199

23119

19820

\begin{align*} \left (x -3 y+4\right ) y^{\prime }&=2 x -6 y+7 \\ \end{align*}

19.203

23120

13965

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

19.210

23121

24938

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

19.216

23122

25615

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

19.221

23123

6583

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

19.237

23124

4440

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

19.241

23125

9650

\begin{align*} y^{\prime \prime }+4 y^{\prime }+13 y&=\delta \left (t -\pi \right )+\delta \left (t -3 \pi \right ) \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

19.246

23126

23895

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

19.250

23127

15183

\begin{align*} \left (2 \sin \left (x \right )-\cos \left (x \right )\right ) y^{\prime \prime }+\left (7 \sin \left (x \right )+4 \cos \left (x \right )\right ) y^{\prime }+10 \cos \left (x \right ) y&=0 \\ \end{align*}

19.251

23128

14916

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

19.262

23129

17654

\begin{align*} 9 x^{2} y^{\prime \prime }+27 y^{\prime } x +10 y&=\frac {1}{x} \\ y \left (1\right ) &= 0 \\ y^{\prime }\left (1\right ) &= -1 \\ \end{align*}

19.276

23130

21088

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

19.277

23131

26200

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

19.283

23132

23013

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

19.300

23133

13975

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

19.306

23134

13338

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

19.313

23135

27135

\(\left [\begin {array}{ccc} 3 & 2 & 0 \\ 2 & 0 & i \\ 0 & -i & 0 \end {array}\right ]\)

N/A

N/A

N/A

19.316

23136

27364

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

19.322

23137

8199

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

19.327

23138

16321

\begin{align*} 1+{\mathrm e}^{y}+x \,{\mathrm e}^{y} y^{\prime }&=0 \\ \end{align*}

19.329

23139

25305

\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=\left \{\begin {array}{cc} {\mathrm e}^{-t} & 0\le t <4 \\ 0 & 4\le t \end {array}\right . \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

19.329

23140

7341

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

19.343

23141

14437

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

19.344

23142

24952

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

19.355

23143

27469

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

19.369

23144

15254

\begin{align*} t^{2} y^{\prime \prime }+3 y^{\prime } t +y&=t^{7} \\ \end{align*}

19.378

23145

6065

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

19.402

23146

12133

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

19.408

23147

20979

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

19.418

23148

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*}

19.447

23149

8301

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

19.454

23150

15828

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

19.459

23151

27202

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

19.465

23152

6842

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

19.466

23153

16437

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

19.470

23154

24794

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

19.480

23155

22375

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

19.485

23156

13400

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

19.488

23157

25773

\begin{align*} y^{\prime }&={\mathrm e}^{-\frac {x y^{2}}{100}} \\ y \left (0\right ) &= -4 \\ \end{align*}

19.495

23158

9139

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

19.498

23159

13651

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

19.502

23160

18596

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

19.510

23161

17987

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

19.516

23162

25423

\begin{align*} y^{\prime }&=-y+\operatorname {Heaviside}\left (t -3\right )+\delta \left (t -1\right ) \\ \end{align*}

19.520

23163

23946

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

19.521

23164

6992

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

19.527

23165

22370

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

19.535

23166

11544

\begin{align*} \left (3 x +2\right ) \left (y-2 x -1\right ) y^{\prime }-y^{2}+y x -7 x^{2}-9 x -3&=0 \\ \end{align*}

19.536

23167

24236

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

19.537

23168

24145

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

19.547

23169

15386

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

19.550

23170

26192

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

19.555

23171

27037

\begin{align*} y^{\prime \prime }-4 y^{\prime }+13 y&=4 \delta \left (t -3\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

19.570

23172

10009

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

19.572

23173

1657

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

19.576

23174

5309

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

19.591

23175

24238

\begin{align*} t x^{\prime }&=6 \,{\mathrm e}^{2 t} t +x \left (2 t -1\right ) \\ \end{align*}

19.592

23176

13403

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

19.605

23177

15235

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

Using Laplace transform method.

19.614

23178

11361

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

19.619

23179

12264

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

19.623

23180

20242

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

19.630

23181

23057

\begin{align*} \left (1+\cos \left (\theta \right )\right ) r^{\prime }&=-r \sin \left (\theta \right ) \\ \end{align*}

19.630

23182

13951

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

19.632

23183

6826

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

19.633

23184

11519

\begin{align*} \left (2 y+x +7\right ) y^{\prime }-y+2 x +4&=0 \\ \end{align*}

19.634

23185

17320

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

19.640

23186

26636

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

19.644

23187

13024

\begin{align*} \left (b +a \sin \left (y\right )^{2}\right ) y^{\prime \prime }+a {y^{\prime }}^{2} \cos \left (y\right ) \sin \left (y\right )+A y \left (c +a \sin \left (y\right )^{2}\right )&=0 \\ \end{align*}

19.648

23188

14041

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

19.650

23189

16436

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

19.656

23190

13422

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

19.657

23191

19397

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

19.658

23192

17970

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

19.689

23193

7561

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

19.695

23194

2347

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

19.703

23195

8727

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

19.721

23196

21055

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

19.728

23197

14026

\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*}

19.730

23198

19964

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

19.737

23199

12486

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

19.763

23200

7322

\begin{align*} x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y&=2 x^{3} \\ \end{align*}

19.765