4.27.10 Problems 901 to 1000

Table 4.1571: Second order, Linear, non-homogeneous and constant coefficients

#

ODE

Mathematica

Maple

Sympy

9661

\[ {} y^{\prime \prime }+4 y^{\prime }+13 y = \delta \left (t -\pi \right )+\delta \left (t -3 \pi \right ) \]

9662

\[ {} y^{\prime \prime }-7 y^{\prime }+6 y = {\mathrm e}^{t}+\delta \left (t -2\right )+\delta \left (t -4\right ) \]

9664

\[ {} y^{\prime \prime }+2 y^{\prime }+10 y = \delta \left (t \right ) \]

9815

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

9816

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

9817

\[ {} y^{\prime \prime }+3 y^{\prime }+2 y = 12 x^{2} \]

9818

\[ {} y^{\prime \prime }+3 y^{\prime }+2 y = x^{2}+2 x +1 \]

9991

\[ {} y^{\prime \prime }-y^{\prime }-2 y = 5 \,{\mathrm e}^{2 x} \]

9992

\[ {} y^{\prime \prime }+16 y = 4 \cos \left (x \right ) \]

9993

\[ {} y^{\prime \prime }-4 y^{\prime }+3 y = 9 x^{2}+4 \]

9994

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

10040

\[ {} y^{\prime \prime }+y^{\prime }+4 y = 1 \]

10041

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

10053

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

10054

\[ {} y^{\prime \prime } = f \left (t \right ) \]

10055

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

10058

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

10081

\[ {} z^{\prime \prime }+3 z^{\prime }+2 z = 24 \,{\mathrm e}^{-3 t}-24 \,{\mathrm e}^{-4 t} \]

10147

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

10148

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

10149

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

10150

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

10151

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

10152

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

10153

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

10154

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

10155

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

10156

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

10157

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

10246

\[ {} y^{\prime \prime }+20 y^{\prime }+500 y = 100000 \cos \left (100 x \right ) \]

10263

\[ {} y^{\prime \prime }+2 y^{\prime }-24 y = 16-\left (x +2\right ) {\mathrm e}^{4 x} \]

10264

\[ {} y^{\prime \prime }+3 y^{\prime }-4 y = 6 \,{\mathrm e}^{2 t -2} \]

10378

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

10379

\[ {} {y^{\prime \prime }}^{2} = 1 \]

10380

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

10381

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

10386

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

10389

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

10395

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

10396

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

10397

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

10398

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

10399

\[ {} y^{\prime \prime }+y^{\prime }+y = x^{3}+x^{2}+x +1 \]

10400

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

10401

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

10402

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

10403

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

10404

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

10405

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

10406

\[ {} y^{\prime \prime }+y^{\prime } = x^{3}+x^{2}+x +1 \]

10407

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

10408

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

10409

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

10410

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

10411

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

10412

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

10413

\[ {} y^{\prime \prime }+y = x^{3}+x^{2}+x +1 \]

10414

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

10415

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

12298

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

12299

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

12300

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

12302

\[ {} y^{\prime \prime }-2 y-4 x^{2} {\mathrm e}^{x^{2}} = 0 \]

12303

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

12326

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

12354

\[ {} y^{\prime \prime }+a y^{\prime }+\tan \left (x \right )+b y = 0 \]

14211

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

14213

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

14214

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

14216

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

14218

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

14219

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

14220

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

14221

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

14222

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

14223

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

14227

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

14233

\[ {} 6 y-5 y^{\prime }+y^{\prime \prime } = \cos \left (x \right )-{\mathrm e}^{2 x} \]

14235

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

14240

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

14241

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

14243

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

14272

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

14319

\[ {} x^{\prime \prime } = -3 \sqrt {t} \]

14377

\[ {} x^{\prime \prime }+x^{\prime } = 3 t \]

14409

\[ {} x^{\prime \prime }+x^{\prime }+x = 3 t^{3}-1 \]

14410

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

14411

\[ {} x^{\prime \prime }+x^{\prime }+x = 12 \]

14412

\[ {} x^{\prime \prime }+x^{\prime }+x = t^{2} {\mathrm e}^{3 t} \]

14413

\[ {} x^{\prime \prime }+x^{\prime }+x = 5 \sin \left (7 t \right ) \]

14414

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

14415

\[ {} x^{\prime \prime }+x^{\prime }+x = t \,{\mathrm e}^{-t} \sin \left (\pi t \right ) \]

14416

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

14417

\[ {} x^{\prime \prime }+x^{\prime }+x = 4 t +5 \,{\mathrm e}^{-t} \]

14418

\[ {} x^{\prime \prime }+x^{\prime }+x = 5 \sin \left (2 t \right )+t \,{\mathrm e}^{t} \]

14419

\[ {} x^{\prime \prime }+x^{\prime }+x = t^{3}+1-4 \cos \left (t \right ) t \]

14420

\[ {} x^{\prime \prime }+x^{\prime }+x = -6+2 \,{\mathrm e}^{2 t} \sin \left (t \right ) \]

14421

\[ {} x^{\prime \prime }+7 x = t \,{\mathrm e}^{3 t} \]

14422

\[ {} x^{\prime \prime }-x^{\prime } = 6+{\mathrm e}^{2 t} \]

14423

\[ {} x^{\prime \prime }+x = t^{2} \]