2.3.52 Problems 5101 to 5200

Table 2.677: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

5101

5956

\begin{align*} x^{2} y^{\prime \prime }&=12 y \\ \end{align*}

0.348

5102

6251

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

0.348

5103

6569

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

0.348

5104

6634

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

0.348

5105

8968

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

Series expansion around \(x=0\).

0.348

5106

10074

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

0.348

5107

10246

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

Series expansion around \(x=0\).

0.348

5108

10400

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

0.348

5109

10448

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

0.348

5110

10649

\begin{align*} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x \left (-x^{2}+5\right ) y^{\prime }-\left (25 x^{2}+7\right ) y&=0 \\ \end{align*}

0.348

5111

10687

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

0.348

5112

13180

\(\left [\begin {array}{cc} -1 & 4 \\ -1 & 3 \end {array}\right ]\)

N/A

N/A

N/A

0.348

5113

13880

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

0.348

5114

16721

\begin{align*} x^{2} y^{\prime \prime }-6 y&=0 \\ \end{align*}

0.348

5115

18183

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

0.348

5116

18199

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

0.348

5117

18771

\begin{align*} y^{\prime \prime }-4 y^{\prime }+16 y&=0 \\ \end{align*}

0.348

5118

19775

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

0.348

5119

22289

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

0.348

5120

22492

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

0.348

5121

23393

\begin{align*} x^{5} y^{\left (5\right )}+3 x^{3} y^{\prime \prime \prime }-9 x^{2} y^{\prime \prime }+18 y^{\prime } x -18 y&=0 \\ \end{align*}

0.348

5122

23805

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

0.348

5123

333

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

0.349

5124

434

\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+8 y^{\prime } x +12 y&=0 \\ \end{align*}

Series expansion around \(x=0\).

0.349

5125

596

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

With initial conditions

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

0.349

5126

1062

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

Series expansion around \(x=0\).

0.349

5127

1063

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

Series expansion around \(x=0\).

0.349

5128

1066

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

Series expansion around \(x=0\).

0.349

5129

1377

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

Series expansion around \(x=0\).

0.349

5130

1458

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

With initial conditions

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

0.349

5131

2226

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-4 y^{\prime } x +4 y&=12 x^{2} \\ \end{align*}

0.349

5132

4132

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

0.349

5133

4650

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

0.349

5134

8849

\begin{align*} x_{1}^{\prime }&=3 x_{1}-18 x_{2} \\ x_{2}^{\prime }&=2 x_{1}-9 x_{2} \\ \end{align*}

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 2 \\ \end{align*}

0.349

5135

11086

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

0.349

5136

11148

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

0.349

5137

16541

\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }+9 y^{\prime \prime }+9 y^{\prime }&=0 \\ y \left (0\right ) &= 10 \\ y^{\prime }\left (0\right ) &= 0 \\ y^{\prime \prime }\left (0\right ) &= 6 \\ y^{\prime \prime \prime }\left (0\right ) &= -60 \\ \end{align*}

0.349

5138

17017

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

0.349

5139

17602

\begin{align*} y^{\left (6\right )}+y^{\prime \prime \prime \prime }&=-24 \\ \end{align*}

0.349

5140

18961

\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime }+16 y&=g \left (t \right ) \\ y \left (0\right ) &= 2 \\ 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.

0.349

5141

19030

\begin{align*} x_{1}^{\prime }&=-3 x_{1}+\frac {5 x_{2}}{2} \\ x_{2}^{\prime }&=-\frac {5 x_{1}}{2}+2 x_{2} \\ \end{align*}

0.349

5142

21518

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

0.349

5143

21919

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

Using Laplace transform method.

0.349

5144

22501

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

0.349

5145

22811

\begin{align*} y^{\prime \prime }+9 y&=20 \,{\mathrm e}^{-t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

Using Laplace transform method.

0.349

5146

24604

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

0.349

5147

24623

\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=18 x \,{\mathrm e}^{-x} \\ \end{align*}

0.349

5148

25119

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

0.349

5149

25621

\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=12 \\ \end{align*}

0.349

5150

27766

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

Series expansion around \(x=0\).

0.349

5151

1372

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

Series expansion around \(x=0\).

0.350

5152

3179

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

0.350

5153

4165

\begin{align*} y_{1}^{\prime }&=y_{2} \\ y_{2}^{\prime }&=3 y_{2}-2 y_{1} \\ \end{align*}

0.350

5154

5767

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

0.350

5155

8813

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

0.350

5156

10133

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

0.350

5157

10508

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

0.350

5158

10600

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

0.350

5159

11729

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

0.350

5160

13724

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

0.350

5161

13786

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

0.350

5162

15703

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

Using Laplace transform method.

0.350

5163

21743

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

0.350

5164

25286

\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=\left \{\begin {array}{cc} {\mathrm e}^{t} & 0\le t <1 \\ {\mathrm e}^{2 t} & 1\le t <\infty \end {array}\right . \\ \end{align*}

Using Laplace transform method.

0.350

5165

2381

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

0.351

5166

2571

\begin{align*} 9 y^{\prime \prime }-12 y^{\prime }+4 y&=0 \\ y \left (\pi \right ) &= 0 \\ y^{\prime }\left (\pi \right ) &= 2 \\ \end{align*}

0.351

5167

3941

\begin{align*} y^{\prime \prime }-y&=12 \,{\mathrm e}^{2 t} \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 1 \\ \end{align*}

Using Laplace transform method.

0.351

5168

7883

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

0.351

5169

8035

\begin{align*} y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }-10 y&=0 \\ \end{align*}

0.351

5170

10385

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

0.351

5171

10950

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

0.351

5172

12599

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

0.351

5173

14415

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

0.351

5174

16583

\begin{align*} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+7 x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\ \end{align*}

0.351

5175

17649

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

0.351

5176

18451

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

0.351

5177

21491

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

0.351

5178

22149

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

0.351

5179

22238

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

Using Laplace transform method.

0.351

5180

22635

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

0.351

5181

23315

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

0.351

5182

23770

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

With initial conditions

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

0.351

5183

26697

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

0.351

5184

27677

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=\frac {1}{{\mathrm e}^{x}+1} \\ \end{align*}

0.351

5185

1010

\begin{align*} x_{1}^{\prime }&=x_{1}-2 x_{2} \\ x_{2}^{\prime }&=2 x_{1}+5 x_{2} \\ \end{align*}

0.352

5186

1457

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

With initial conditions

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

0.352

5187

2390

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

0.352

5188

2787

\begin{align*} x_{1}^{\prime }&=3 x_{1} \\ x_{2}^{\prime }&=x_{1}+3 x_{2} \\ x_{3}^{\prime }&=3 x_{3} \\ x_{4}^{\prime }&=2 x_{3}+3 x_{4} \\ \end{align*}

With initial conditions

\begin{align*} x_{1} \left (0\right ) &= 1 \\ x_{2} \left (0\right ) &= 1 \\ x_{3} \left (0\right ) &= 1 \\ x_{4} \left (0\right ) &= 1 \\ \end{align*}

0.352

5189

3337

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

Series expansion around \(x=1\).

0.352

5190

6179

\begin{align*} -\left (5+4 x \right ) y+32 y^{\prime } x +16 x^{2} y^{\prime \prime }&=0 \\ \end{align*}

0.352

5191

6694

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

0.352

5192

6781

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

0.352

5193

7142

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

0.352

5194

8006

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

0.352

5195

9274

\begin{align*} y^{\prime \prime }-y^{\prime }-6 y&={\mathrm e}^{-x} \\ \end{align*}

0.352

5196

9442

\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=5 \,{\mathrm e}^{3 t} \\ y \left (0\right ) &= 0 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

Using Laplace transform method.

0.352

5197

10139

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

0.352

5198

10238

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

0.352

5199

10560

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

0.352

5200

10765

\begin{align*} y^{\prime \prime }-2 y^{\prime } x +8 y&=0 \\ \end{align*}

0.352