2.3.253 Problems 25201 to 25300

Table 2.1089: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

25201

11556

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (t -1\right ) y^{\prime \prime }-y^{\prime } t +y&=2 t \,{\mathrm e}^{-t}\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]

35.858

25202

19719

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (t -1\right ) y^{\prime \prime }-y^{\prime } t +y&=2 t \,{\mathrm e}^{-t}\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]

35.861

25203

25693

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (t -1\right ) y^{\prime \prime }-y^{\prime } t +y&=2 t \,{\mathrm e}^{-t}\\ y \left (0\right )&=a\\ y^{\prime }\left (0\right )&=b\\ \end {array} \]

35.876

25204

792

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-4 y^{\prime } t +6 y&=t^{5} \end {array} \]

35.905

25205

13808

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-4 y^{\prime } t +6 y&=0 \end {array} \]

35.917

25206

4789

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-4 y^{\prime } t +6 y&=t^{5}\\ y \left (1\right )&=1\\ y^{\prime }\left (1\right )&=0\\ \end {array} \]

35.925

25207

12622

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-4 y^{\prime } t +6 y&=t^{5}\\ y \left (1\right )&=0\\ y^{\prime }\left (1\right )&=1\\ \end {array} \]

35.931

25208

18572

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-4 y^{\prime } t +6 y&=t^{5}\\ y \left (1\right )&=-1\\ y^{\prime }\left (1\right )&=3\\ \end {array} \]

35.935

25209

22992

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-4 y^{\prime } t +6 y&=t^{5}\\ y \left (1\right )&=a\\ y^{\prime }\left (1\right )&=b\\ \end {array} \]

35.958

25210

11700

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+3 y^{\prime } t -4 y&=t^{4}\\ y \left (-1\right )&=y_{1}\\ y^{\prime }\left (-1\right )&=y_{1}\\ \end {array} \]

35.996

25211

19351

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }-2 y&=\frac {t^{2}+1}{-t^{2}+1}\\ y \left (2\right )&=y_{1}\\ y^{\prime }\left (2\right )&=y_{1}\\ \end {array} \]

36.003

25212

6256

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \sin \left (t \right ) y^{\prime \prime }+y&=\cos \left (t \right )\\ y \left (\frac {\pi }{2}\right )&=y_{1}\\ y^{\prime }\left (\frac {\pi }{2}\right )&=y_{1}\\ \end {array} \]

36.016

25213

9736

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (t^{2}+1\right ) y^{\prime \prime }-y^{\prime } t +t^{2} y&=\cos \left (t \right )\\ y \left (0\right )&=y_{1}\\ y^{\prime }\left (0\right )&=y_{1}\\ \end {array} \]

36.020

25214

11726

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\sqrt {t}\, y^{\prime }-\sqrt {t -3}\, y&=0\\ y \left (10\right )&=y_{1}\\ y^{\prime }\left (10\right )&=y_{1}\\ \end {array} \]

36.020

25215

13892

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t \left (t^{2}-4\right ) y^{\prime \prime }+y&={\mathrm e}^{t}\\ y \left (1\right )&=y_{1}\\ y^{\prime }\left (1\right )&=y_{1}\\ \end {array} \]

36.038

25216

17214

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-4 y^{\prime } t +6 y&=0\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]

36.038

25217

11686

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+a_{1} \left (t \right ) y^{\prime }+a_{0} \left (t \right ) y&=f \left (t \right ) \end {array} \]

36.046

25218

15628

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (t -1\right ) y^{\prime \prime }-y^{\prime } t +y&=0 \end {array} \]

36.067

25219

16227

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (t^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } t +2 y&=0 \end {array} \]

36.073

25220

16350

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+y^{\prime } t +4 y&=0 \end {array} \]

36.075

25221

17270

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-2 y^{\prime } t&=0 \end {array} \]

36.076

25222

22087

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+2 y^{\prime } t -2 y&=0 \end {array} \]

36.081

25223

2339

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 t^{2} y^{\prime \prime }-5 y^{\prime } t +3 y&=0 \end {array} \]

36.140

25224

19674

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 9 t^{2} y^{\prime \prime }+3 y^{\prime } t +y&=0 \end {array} \]

36.181

25225

22386

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+y^{\prime } t -2 y&=0 \end {array} \]

36.187

25226

15895

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 t^{2} y^{\prime \prime }+y&=0 \end {array} \]

36.201

25227

7532

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-3 y^{\prime } t -21 y&=0 \end {array} \]

36.213

25228

9095

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+7 y^{\prime } t +9 y&=0 \end {array} \]

36.243

25229

2876

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+y&=0 \end {array} \]

36.273

25230

14869

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+y^{\prime } t -4 y&=0 \end {array} \]

36.279

25231

16894

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+y^{\prime } t +4 y&=0 \end {array} \]

36.311

25232

19124

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-3 y^{\prime } t +13 y&=0 \end {array} \]

36.315

25233

7419

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+2 y^{\prime } t -2 y&=0\\ y \left (1\right )&=0\\ y^{\prime }\left (1\right )&=1\\ \end {array} \]

36.384

25234

18287

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 t^{2} y^{\prime \prime }+y&=0\\ y \left (1\right )&=2\\ y^{\prime }\left (1\right )&=0\\ \end {array} \]

36.398

25235

15634

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+y^{\prime } t +4 y&=0\\ y \left (1\right )&=-3\\ y^{\prime }\left (1\right )&=4\\ \end {array} \]

36.402

25236

21164

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-4 y^{\prime } t +6 y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-1\\ \end {array} \]

36.404

25237

11940

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }+\left (t -1\right ) y^{\prime }-y&=0 \end {array} \]

Using Laplace transform method.

36.438

25238

1660

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }+\left (1+t \right ) y^{\prime }+y&=0 \end {array} \]

Using Laplace transform method.

36.569

25239

13523

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }+\left (2+4 t \right ) y^{\prime }+\left (4+4 t \right ) y&=0 \end {array} \]

Using Laplace transform method.

36.582

25240

15946

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }-2 y^{\prime }+t y&=0 \end {array} \]

Using Laplace transform method.

36.625

25241

19950

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }-4 y^{\prime }+t y&=0\\ y \left (0\right )&=0\\ \end {array} \]

Using Laplace transform method.

36.630

25242

23837

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }+\left (2 t +2\right ) y^{\prime }+\left (t +2\right ) y&=0 \end {array} \]

Using Laplace transform method.

36.644

25243

22529

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -t y^{\prime \prime }+\left (-2+t \right ) y^{\prime }+y&=0 \end {array} \]

Using Laplace transform method.

36.654

25244

1727

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -t y^{\prime \prime }-2 y^{\prime }+t y&=0 \end {array} \]

Using Laplace transform method.

36.676

25245

16156

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }+\left (2-5 t \right ) y^{\prime }+\left (6 t -5\right ) y&=0 \end {array} \]

Using Laplace transform method.

36.704

25246

1711

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }+2 y^{\prime }+9 t y&=0 \end {array} \]

Using Laplace transform method.

36.713

25247

5179

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime \prime }+3 y^{\prime \prime }+y^{\prime } t +y&=0 \end {array} \]

Using Laplace transform method.

36.717

25248

1624

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }+\left (t +2\right ) y^{\prime }+y&=0 \end {array} \]

Using Laplace transform method.

36.741

25249

23842

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-3 y^{\prime } t +4 y&=0 \end {array} \]

36.760

25250

5986

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+2 y^{\prime } t -2 y&=0 \end {array} \]

36.767

25251

22094

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 t^{2} y^{\prime \prime }+y&=0 \end {array} \]

36.773

25252

14139

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+2 y^{\prime } t&=0 \end {array} \]

36.778

25253

15865

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-t \left (t +2\right ) y^{\prime }+\left (t +2\right ) y&=0 \end {array} \]

36.800

25254

23207

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-4 y^{\prime } t +\left (t^{2}+6\right ) y&=0 \end {array} \]

36.829

25255

163

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }-y^{\prime }+4 t^{3} y&=0 \end {array} \]

36.841

25256

9755

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }-2 \left (1+t \right ) y^{\prime }+4 y&=0 \end {array} \]

36.846

25257

10073

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 \sec \left (t \right )^{2} y&=0 \end {array} \]

36.883

25258

23216

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }+\left (t -1\right ) y^{\prime }-y&=0 \end {array} \]

36.911

25259

14526

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-\tan \left (t \right ) y^{\prime }-\sec \left (t \right )^{2} y&=0 \end {array} \]

36.922

25260

13036

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (t^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } t +2 y&=0 \end {array} \]

36.933

25261

13970

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (1+\cos \left (2 t \right )\right ) y^{\prime \prime }-4 y&=0 \end {array} \]

36.941

25262

21319

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-2 y^{\prime } t +\left (t^{2}+2\right ) y&=0 \end {array} \]

36.944

25263

9750

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-t^{2}+1\right ) y^{\prime \prime }+2 y&=0 \end {array} \]

36.954

25264

13797

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-t^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } t +2 y&=0 \end {array} \]

36.957

25265

13428

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\sin \left (t \right ) \end {array} \]

37.005

25266

13633

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y&={\mathrm e}^{2 t} \end {array} \]

37.027

25267

23756

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }+5 y&={\mathrm e}^{t} \end {array} \]

37.060

25268

17254

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y^{\prime }&={\mathrm e}^{-3 t} \end {array} \]

37.072

25269

18499

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-3 y^{\prime }+2 y&={\mathrm e}^{3 t} \end {array} \]

37.074

25270

8697

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\tan \left (t \right ) \end {array} \]

37.089

25271

15480

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }+y&=\frac {{\mathrm e}^{t}}{t} \end {array} \]

37.119

25272

5261

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\sec \left (t \right ) \end {array} \]

37.129

25273

25876

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-2 y^{\prime } t +2 y&=t^{4} \end {array} \]

37.163

25274

4788

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }-y^{\prime }&=3 t^{2}-1 \end {array} \]

37.197

25275

23133

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-y^{\prime } t +y&=t \end {array} \]

37.223

25276

11643

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y^{\prime }+4 y&=\frac {{\mathrm e}^{2 t}}{t^{2}+1} \end {array} \]

37.228

25277

8245

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-\tan \left (t \right ) y^{\prime }-\sec \left (t \right )^{2} y&=t \end {array} \]

37.270

25278

12113

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }+\left (t -1\right ) y^{\prime }-y&={\mathrm e}^{-t} t^{2} \end {array} \]

37.276

25279

25899

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }-y^{\prime }+4 t^{3} y&=4 t^{5} \end {array} \]

37.310

25280

12970

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y&=\frac {1}{1+{\mathrm e}^{-t}} \end {array} \]

37.319

25281

23018

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+a^{2} y&=f \left (t \right ) \end {array} \]

Using Laplace transform method.

37.320

25282

8824

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-a^{2} y&=f \left (t \right ) \end {array} \]

Using Laplace transform method.

37.347

25283

11598

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 a y^{\prime }+a^{2} y&=f \left (t \right ) \end {array} \]

Using Laplace transform method.

37.355

25284

6088

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-\left (a +b \right ) y^{\prime }+a b y&=f \left (t \right ) \end {array} \]

Using Laplace transform method.

37.357

25285

9990

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=\left \{\begin {array}{cc} 4 & 0\le t <2 \\ 8 t & 2\le t <\infty \end {array}\right . \end {array} \]

Using Laplace transform method.

37.367

25286

3546

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-3 y^{\prime }+2 y&=\left \{\begin {array}{cc} {\mathrm e}^{t} & 0\le t <1 \\ {\mathrm e}^{2 t} & 1\le t <\infty \end {array}\right . \end {array} \]

Using Laplace transform method.

37.369

25287

1725

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -y+y^{\prime }&=\left \{\begin {array}{cc} 1 & 0\le t <2 \\ -1 & 2\le t <4 \\ 0 & 4\le t <\infty \end {array}\right .\\ y \left (0\right )&=0\\ \end {array} \]

Using Laplace transform method.

37.372

25288

20722

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 y+y^{\prime }&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 1 & 1\le t <\infty \end {array}\right .\\ y \left (0\right )&=0\\ \end {array} \]

Using Laplace transform method.

37.384

25289

22010

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -y+y^{\prime }&=\left \{\begin {array}{cc} 0 & 0\le t <1 \\ t -1 & 1\le t <2 \\ 3-t & 2\le t <3 \\ 0 & 3\le t <\infty \end {array}\right .\\ y \left (0\right )&=0\\ \end {array} \]

Using Laplace transform method.

37.388

25290

21826

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+y^{\prime }&=\left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\pi \\ 0 & \pi \le t <\infty \end {array}\right .\\ y \left (\pi \right )&=-1\\ \end {array} \]

Using Laplace transform method.

37.406

25291

25694

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t <\infty \end {array}\right .\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]

Using Laplace transform method.

37.427

25292

15828

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y^{\prime }+4 y&=\left \{\begin {array}{cc} 0 & 0\le t <2 \\ 4 & 2\le t <\infty \end {array}\right .\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]

Using Laplace transform method.

37.448

25293

11511

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\left \{\begin {array}{cc} 0 & t =0 \\ \sin \left (\frac {1}{t}\right ) & \operatorname {otherwise} \end {array}\right . \end {array} \]

Using Laplace transform method.

37.480

25294

15350

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+2 y&=\left \{\begin {array}{cc} 0 & 0\le t <1 \\ -3 & 1\le t \end {array}\right .\\ y \left (0\right )&=0\\ \end {array} \]

Using Laplace transform method.

37.490

25295

24331

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+5 y&=\left \{\begin {array}{cc} -5 & 0\le t <1 \\ 5 & 1\le t \end {array}\right .\\ y \left (0\right )&=1\\ \end {array} \]

Using Laplace transform method.

37.504

25296

14439

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-3 y&=\left \{\begin {array}{cc} 0 & 0\le t <2 \\ 2 & 2\le t <3 \\ 0 & 3\le t \end {array}\right .\\ y \left (0\right )&=0\\ \end {array} \]

Using Laplace transform method.

37.516

25297

11363

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+2 y&=\left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right .\\ y \left (0\right )&=0\\ \end {array} \]

Using Laplace transform method.

37.532

25298

15891

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-4 y&=\left \{\begin {array}{cc} 12 \,{\mathrm e}^{t} & 0\le t <1 \\ 12 \,{\mathrm e} & 1\le t \end {array}\right .\\ y \left (0\right )&=2\\ \end {array} \]

Using Laplace transform method.

37.553

25299

2887

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 y+y^{\prime }&=\left \{\begin {array}{cc} 10 \sin \left (t \right ) & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right .\\ y \left (0\right )&=-1\\ \end {array} \]

Using Laplace transform method.

37.555

25300

26307

\[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+9 y&=\operatorname {Heaviside}\left (t -3\right )\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]

Using Laplace transform method.

37.586