4.2.41 Problems 4001 to 4100

Table 4.249: Second order linear ODE

#

ODE

Mathematica

Maple

Sympy

14068

\[ {} x y^{\prime \prime }+y^{\prime }+y = 0 \]

14069

\[ {} x y^{\prime \prime }+x^{2} y = 0 \]

14070

\[ {} y^{\prime \prime }+\alpha ^{2} y = 0 \]

14071

\[ {} y^{\prime \prime }-\alpha ^{2} y = 0 \]

14072

\[ {} y^{\prime \prime }+\beta y^{\prime }+\gamma y = 0 \]

14073

\[ {} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+n \left (n +1\right ) y = 0 \]

14074

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }+\left (-\nu ^{2}+x^{2}\right ) y = \sin \left (x \right ) \]

14080

\[ {} y^{\prime \prime }-2 k y^{\prime }+k^{2} y = {\mathrm e}^{x} \]

14081

\[ {} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }-a^{2} y = 0 \]

14082

\[ {} y^{\prime \prime }+\frac {2 y^{\prime }}{x} = 0 \]

14149

\[ {} y^{\prime \prime } = a^{2} y \]

14151

\[ {} x y^{\prime \prime }-y^{\prime } = x^{2} {\mathrm e}^{x} \]

14153

\[ {} y^{\prime \prime }+\tan \left (x \right ) y^{\prime } = \sin \left (2 x \right ) \]

14158

\[ {} y^{\prime \prime } = 9 y \]

14159

\[ {} y^{\prime \prime }+y = 0 \]

14160

\[ {} y^{\prime \prime }-y = 0 \]

14161

\[ {} y^{\prime \prime }+12 y = 7 y^{\prime } \]

14162

\[ {} y^{\prime \prime }-4 y^{\prime }+4 y = 0 \]

14163

\[ {} y^{\prime \prime }+2 y^{\prime }+10 y = 0 \]

14164

\[ {} y^{\prime \prime }+3 y^{\prime }-2 y = 0 \]

14165

\[ {} 4 y^{\prime \prime }-12 y^{\prime }+9 y = 0 \]

14166

\[ {} y^{\prime \prime }+y^{\prime }+y = 0 \]

14175

\[ {} y^{\prime \prime }-7 y^{\prime }+12 y = x \]

14176

\[ {} s^{\prime \prime }-a^{2} s = t +1 \]

14177

\[ {} y^{\prime \prime }+y^{\prime }-2 y = 8 \sin \left (2 x \right ) \]

14178

\[ {} y^{\prime \prime }-y = 5 x +2 \]

14179

\[ {} y^{\prime \prime }-2 a y^{\prime }+a^{2} y = {\mathrm e}^{x} \]

14180

\[ {} y^{\prime \prime }+6 y^{\prime }+5 y = {\mathrm e}^{2 x} \]

14181

\[ {} y^{\prime \prime }+9 y = 6 \,{\mathrm e}^{3 x} \]

14182

\[ {} y^{\prime \prime }-3 y^{\prime } = 2-6 x \]

14183

\[ {} y^{\prime \prime }-2 y^{\prime }+3 y = {\mathrm e}^{-x} \cos \left (x \right ) \]

14184

\[ {} y^{\prime \prime }+4 y = 2 \sin \left (2 x \right ) \]

14188

\[ {} y^{\prime \prime }+2 h y^{\prime }+n^{2} y = 0 \]

14189

\[ {} y^{\prime \prime }+n^{2} y = h \sin \left (r x \right ) \]

14190

\[ {} y^{\prime \prime }-7 y^{\prime }+6 y = \sin \left (x \right ) \]

14191

\[ {} y^{\prime \prime }+y = \sec \left (x \right ) \]

14192

\[ {} y^{\prime \prime }+y = \frac {1}{\cos \left (2 x \right )^{{3}/{2}}} \]

14199

\[ {} y^{\prime \prime }+y = \sec \left (x \right ) \]

14202

\[ {} y^{\prime \prime }-4 y = {\mathrm e}^{2 x} \sin \left (2 x \right ) \]

14231

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \]

14233

\[ {} 2 x^{2} y^{\prime \prime }+3 x y^{\prime }-y = 0 \]

14234

\[ {} y^{\prime \prime }-3 y^{\prime }+2 y = 0 \]

14235

\[ {} x^{2} y^{\prime \prime }-2 y = 0 \]

14241

\[ {} 2 x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \]

14244

\[ {} y^{\prime \prime }-3 y^{\prime }-10 y = 0 \]

14245

\[ {} y^{\prime \prime }+2 y^{\prime }+y = 0 \]

14248

\[ {} x^{2} y^{\prime \prime }-x y^{\prime } = 0 \]

14249

\[ {} x^{2} y^{\prime \prime }+6 x y^{\prime }+4 y = 0 \]

14250

\[ {} x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 0 \]

14256

\[ {} y^{\prime \prime }-y^{\prime }-6 y = 0 \]

14258

\[ {} y^{\prime \prime }-y = 0 \]

14261

\[ {} y^{\prime \prime }-y^{\prime }-2 y = 0 \]

14262

\[ {} y^{\prime \prime }-y^{\prime }-2 y = 0 \]

14263

\[ {} y^{\prime \prime }-y^{\prime }-2 y = 0 \]

14264

\[ {} y^{\prime \prime }-y^{\prime }-2 y = 0 \]

14266

\[ {} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \]

14267

\[ {} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \]

14268

\[ {} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \]

14269

\[ {} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \]

14270

\[ {} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \]

14271

\[ {} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \]

14401

\[ {} 3 y^{\prime \prime }-2 y^{\prime }+4 y = x \]

14403

\[ {} x \left (x -3\right ) y^{\prime \prime }+3 y^{\prime } = x^{2} \]

14404

\[ {} x \left (x -3\right ) y^{\prime \prime }+3 y^{\prime } = x^{2} \]

14405

\[ {} \sqrt {1-x}\, y^{\prime \prime }-4 y = \sin \left (x \right ) \]

14406

\[ {} \left (x^{2}-4\right ) y^{\prime \prime }+y \ln \left (x \right ) = x \,{\mathrm e}^{x} \]

14407

\[ {} y^{\prime \prime }-y = 0 \]

14408

\[ {} y^{\prime \prime }+y = 0 \]

14409

\[ {} x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y = 0 \]

14411

\[ {} y^{\prime \prime }-y = 0 \]

14413

\[ {} x^{2} y^{\prime \prime }-x y^{\prime }+y = 0 \]

14414

\[ {} y^{\prime \prime }-4 y = 31 \]

14415

\[ {} y^{\prime \prime }+9 y = 27 x +18 \]

14416

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }-4 y = -3 x -\frac {3}{x} \]

14417

\[ {} 4 y^{\prime \prime }+4 y^{\prime }-3 y = 0 \]

14427

\[ {} y^{\prime \prime }+\alpha y = 0 \]

14443

\[ {} y^{\prime \prime }-2 y^{\prime }+5 y = 0 \]

14445

\[ {} y^{\prime \prime }-9 y = 2 \sin \left (3 x \right ) \]

14446

\[ {} y^{\prime \prime }+9 y = 2 \sin \left (3 x \right ) \]

14447

\[ {} y^{\prime \prime }+y^{\prime }-2 y = x \,{\mathrm e}^{x}-3 x^{2} \]

14451

\[ {} y^{\prime \prime }-9 y = x +2 \]

14452

\[ {} y^{\prime \prime }+9 y = x +2 \]

14453

\[ {} y^{\prime \prime }-y^{\prime }+6 y = -2 \sin \left (3 x \right ) \]

14454

\[ {} y^{\prime \prime }-2 y^{\prime }+2 y = -x^{2}+1 \]

14458

\[ {} y^{\prime \prime }+9 y = 1 \]

14459

\[ {} y^{\prime \prime }+9 y = 18 \,{\mathrm e}^{3 x} \]

14460

\[ {} y^{\prime \prime }-y^{\prime }-2 y = 0 \]

14461

\[ {} y^{\prime \prime }-y^{\prime }-2 y = x^{2} \]

14462

\[ {} y^{\prime \prime }-2 y^{\prime }+y = 2 \sin \left (x \right ) \]

14465

\[ {} y^{\prime \prime }-y^{\prime }-2 y = \left \{\begin {array}{cc} 1 & 2\le x <4 \\ 0 & \operatorname {otherwise} \end {array}\right . \]

14466

\[ {} y^{\prime \prime }-2 y^{\prime } = \left \{\begin {array}{cc} 0 & 0\le x <1 \\ \left (x -1\right )^{2} & 1\le x \end {array}\right . \]

14467

\[ {} y^{\prime \prime }-2 y^{\prime }+y = \left \{\begin {array}{cc} 0 & 0\le x <1 \\ x^{2}-2 x +3 & 1\le x \end {array}\right . \]

14468

\[ {} y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 0 & 0\le x <\pi \\ -\sin \left (3 x \right ) & \pi \le x \end {array}\right . \]

14469

\[ {} y^{\prime \prime }-4 y = \left \{\begin {array}{cc} x & 0\le x <1 \\ 1 & 1\le x \end {array}\right . \]

14470

\[ {} y^{\prime \prime }-4 y^{\prime }+5 y = \left \{\begin {array}{cc} x & 0\le x <1 \\ 1 & 1\le x \end {array}\right . \]

14473

\[ {} y^{\prime \prime }+9 y = \delta \left (x -\pi \right )+\delta \left (x -3 \pi \right ) \]

14474

\[ {} y^{\prime \prime }-2 y^{\prime }+y = 2 \delta \left (x -1\right ) \]

14475

\[ {} y^{\prime \prime }-2 y^{\prime }+5 y = \cos \left (x \right )+2 \delta \left (x -\pi \right ) \]

14476

\[ {} y^{\prime \prime }+4 y = \cos \left (x \right ) \delta \left (x -\pi \right ) \]

14477

\[ {} y^{\prime \prime }+a^{2} y = \delta \left (x -\pi \right ) f \left (x \right ) \]