2.3.142 Problems 14101 to 14200

Table 2.857: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

14101

1286

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

1.445

14102

3978

\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=\delta \left (t -\frac {\pi }{2}\right ) \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 2 \\ \end{align*}

Using Laplace transform method.

1.445

14103

12640

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

1.445

14104

13741

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

1.446

14105

21226

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

1.446

14106

9860

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

Series expansion around \(x=0\).

1.447

14107

17019

\begin{align*} x^{2} y^{\prime \prime }-x y^{\prime }-16 y&=0 \\ \end{align*}

1.447

14108

21858

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

1.447

14109

9757

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

1.448

14110

23908

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

1.448

14111

13773

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

1.449

14112

14069

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

1.449

14113

675

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

1.450

14114

8991

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

Series expansion around \(x=0\).

1.450

14115

23018

\begin{align*} x^{\prime \prime }+36 x&=0 \\ x \left (0\right ) &= 5 \\ x \left (\frac {\pi }{12}\right ) &= 7 \\ \end{align*}

1.450

14116

6240

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

1.451

14117

7904

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

1.451

14118

22875

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

Series expansion around \(x=0\).

1.451

14119

25564

\begin{align*} y^{\prime \prime }+2 z \omega _{n} y^{\prime }+\omega _{n}^{2} y&={\mathrm e}^{c t} \\ \end{align*}

1.451

14120

25577

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

1.451

14121

5828

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

1.452

14122

9549

\begin{align*} 9 x^{2} y^{\prime \prime }+9 x^{2} y^{\prime }+2 y&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.452

14123

14670

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

1.452

14124

27700

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

1.452

14125

9550

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

Series expansion around \(x=0\).

1.453

14126

20456

\begin{align*} 4 x \left (x -1\right ) \left (x -2\right ) {y^{\prime }}^{2}-\left (3 x^{2}-6 x +2\right )^{2}&=0 \\ \end{align*}

1.453

14127

26639

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

1.453

14128

3981

\begin{align*} y^{\prime \prime }+6 y^{\prime }+13 y&=\delta \left (t -\frac {\pi }{4}\right ) \\ y \left (0\right ) &= 5 \\ y^{\prime }\left (0\right ) &= 5 \\ \end{align*}

Using Laplace transform method.

1.454

14129

8407

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

1.454

14130

16708

\begin{align*} y^{\prime \prime }+36 y&=0 \\ \end{align*}

1.454

14131

19525

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

1.454

14132

20729

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

1.454

14133

12916

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

1.455

14134

14752

\begin{align*} x^{2} y^{\prime \prime }-x y^{\prime }+\left (2 x^{2}+\frac {5}{9}\right ) y&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.456

14135

21894

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

1.456

14136

25184

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

1.456

14137

85

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

1.457

14138

10525

\begin{align*} y^{\prime \prime }+x^{6} y^{\prime }+7 x^{5} y&=0 \\ \end{align*}

1.457

14139

11720

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

1.457

14140

18036

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

1.457

14141

18192

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

1.457

14142

25222

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

1.458

14143

25563

\begin{align*} y^{\prime \prime }+2 z \omega _{n} y^{\prime }+\omega _{n}^{2} y&=0 \\ \end{align*}

1.458

14144

20841

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

1.459

14145

27008

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

1.459

14146

6507

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

1.460

14147

12331

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

1.460

14148

12934

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

1.460

14149

13788

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

1.460

14150

14753

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

Series expansion around \(x=0\).

1.460

14151

16967

\begin{align*} y^{\prime \prime }+9 y^{\prime }&=0 \\ \end{align*}

1.460

14152

19393

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

1.460

14153

24639

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

1.461

14154

25959

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

1.461

14155

2527

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

1.463

14156

9904

\begin{align*} 4 x^{2} y^{\prime \prime }+8 x \left (x +1\right ) y^{\prime }+y&=0 \\ \end{align*}

Series expansion around \(x=0\).

1.463

14157

14631

\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=6 \,{\mathrm e}^{-2 x}+3 \,{\mathrm e}^{x}-4 x^{2} \\ \end{align*}

1.463

14158

2694

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

Using Laplace transform method.

1.464

14159

5663

\begin{align*} 16 y^{2} {y^{\prime }}^{3}+2 x y^{\prime }-y&=0 \\ \end{align*}

1.464

14160

10143

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

1.464

14161

16557

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

1.464

14162

8899

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

1.465

14163

9169

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

1.465

14164

17537

\begin{align*} 4 t^{2} y^{\prime \prime }+4 t y^{\prime }+\left (16 t^{2}-1\right ) y&=16 t^{{3}/{2}} \\ y \left (\pi \right ) &= 0 \\ y^{\prime }\left (2 \pi \right ) &= 0 \\ \end{align*}

1.465

14165

12654

\begin{align*} y^{\prime \prime }&=\frac {\left (7 a \,x^{2}+5\right ) y^{\prime }}{x \left (a \,x^{2}+1\right )}-\frac {\left (15 a \,x^{2}+5\right ) y}{x^{2} \left (a \,x^{2}+1\right )} \\ \end{align*}

1.466

14166

18395

\begin{align*} y^{\prime \prime }+\frac {5 y^{\prime }}{x}+y&=0 \\ \end{align*}

1.466

14167

993

\begin{align*} x_{1}^{\prime }&=2 x_{1} \\ x_{2}^{\prime }&=-21 x_{1}-5 x_{2}-27 x_{3}-9 x_{4} \\ x_{3}^{\prime }&=5 x_{3} \\ x_{4}^{\prime }&=-21 x_{3}-2 x_{4} \\ \end{align*}

1.467

14168

8032

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

1.467

14169

14749

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

Series expansion around \(x=0\).

1.467

14170

18079

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

1.467

14171

19685

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

1.467

14172

217

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

1.468

14173

230

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

1.468

14174

9883

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

1.469

14175

18197

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

1.469

14176

1301

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

1.470

14177

5802

\begin{align*} 16 y+8 y^{\prime }+y^{\prime \prime }&=4 \,{\mathrm e}^{x}-{\mathrm e}^{2 x} \\ \end{align*}

1.470

14178

9931

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

1.470

14179

9965

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

Series expansion around \(x=0\).

1.470

14180

16699

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

1.470

14181

25401

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

1.470

14182

26678

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

1.470

14183

8898

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

1.472

14184

13854

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

1.472

14185

7116

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

1.473

14186

3216

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

1.474

14187

3245

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

1.474

14188

3424

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

1.474

14189

16963

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

1.474

14190

18386

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

Series expansion around \(x=0\).

1.474

14191

21244

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

1.474

14192

14360

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

Using Laplace transform method.

1.475

14193

25283

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

Using Laplace transform method.

1.475

14194

3226

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

1.476

14195

6368

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

1.476

14196

12375

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

1.476

14197

25341

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

Series expansion around \(t=0\).

1.476

14198

4425

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

1.477

14199

13853

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

1.477

14200

16745

\begin{align*} x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y&=18 \ln \left (x \right ) \\ \end{align*}

1.477