4.27.21 Problems 2001 to 2100

Table 4.1593: Second order, Linear, non-homogeneous and constant coefficients

#

ODE

Mathematica

Maple

Sympy

21258

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

21259

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

21260

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

21261

\[ {} x^{\prime \prime }-x = {\mathrm e}^{k t} \]

21262

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

21263

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

21264

\[ {} x^{\prime \prime }-4 x^{\prime }+3 x = 2 \,{\mathrm e}^{t}-5 \,{\mathrm e}^{2 t} \]

21265

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

21266

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

21267

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

21268

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

21269

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

21270

\[ {} x^{\prime \prime }+4 x^{\prime }+x = k \]

21271

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

21399

\[ {} x^{\prime \prime }-4 x^{\prime }+3 x = 1 \]

21404

\[ {} x^{\prime \prime }+x = g \left (t \right ) \]

21405

\[ {} x^{\prime \prime } = \delta \left (-t +a \right ) \]

21594

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

21595

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

21630

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

21631

\[ {} y^{\prime \prime } = 9 x^{2}+2 x -1 \]

21632

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

21633

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

21634

\[ {} y^{\prime \prime }+2 y^{\prime }+5 y = x^{3}+3 \]

21635

\[ {} y^{\prime \prime }+y^{\prime }-6 y = 2 x^{3}+5 x^{2}-7 x +2 \]

21636

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

21637

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

21638

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

21639

\[ {} y^{\prime \prime }-4 y^{\prime }+5 y = 2 \cos \left (x \right ) \]

21640

\[ {} y^{\prime \prime }+2 y^{\prime }+5 y = 3 \sin \left (x +\frac {\pi }{4}\right ) \]

21641

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

21642

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

21643

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

21644

\[ {} y^{\prime \prime }-2 y^{\prime }+y = \left (x^{2}-1\right ) {\mathrm e}^{2 x}+\left (3 x +4\right ) {\mathrm e}^{x} \]

21645

\[ {} y^{\prime \prime }+y^{\prime }+8 y = \left (10 x^{2}+21 x +9\right ) \sin \left (3 x \right )+x \cos \left (3 x \right ) \]

21646

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

21647

\[ {} y^{\prime \prime }+y^{\prime }-2 y = 2 x -40 \cos \left (2 x \right ) \]

21648

\[ {} y^{\prime \prime }-2 y^{\prime }-3 y = 2 \,{\mathrm e}^{x}-10 \sin \left (x \right ) \]

21655

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

21656

\[ {} y^{\prime \prime }-3 y^{\prime }+2 y = \frac {1}{1+{\mathrm e}^{-x}} \]

21657

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

21658

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

21659

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

21660

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

21661

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

21662

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

21663

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

21664

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

21683

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

21688

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

21691

\[ {} y^{\prime \prime }-2 y^{\prime }+5 y = 16 x^{3} {\mathrm e}^{3 x} \]

21693

\[ {} y^{\prime \prime }-2 y^{\prime }+y = x \,{\mathrm e}^{x}+7 x -2 \]

21695

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

21696

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

21697

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

21700

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

21701

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

21702

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

21704

\[ {} y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{2 x} \left (1+x \right ) \]

21707

\[ {} y^{\prime \prime }+y^{\prime }-12 y = x^{2} {\mathrm e}^{x} \]

21734

\[ {} y^{\prime \prime }+2 b y^{\prime }+y = k \]

21737

\[ {} \theta ^{\prime \prime }+4 \theta = 15 \cos \left (3 t \right ) \]

21830

\[ {} y^{\prime \prime }+4 y^{\prime }+8 y = \sin \left (t \right ) \]

21831

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

21832

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

21833

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

21834

\[ {} y^{\prime \prime }-3 y^{\prime }+2 y = \left \{\begin {array}{cc} 0 & t <6 \\ 1 & 6\le t \end {array}\right . \]

21835

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

21836

\[ {} y^{\prime \prime }+2 y^{\prime }+5 y = \left \{\begin {array}{cc} 1 & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right . \]

21874

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

21909

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

21999

\[ {} y^{\prime \prime }-2 y^{\prime }-3 y+8 \,{\mathrm e}^{-x}+3 x = 0 \]

22000

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

22001

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

22002

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

22003

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

22005

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

22007

\[ {} y^{\prime \prime }+6 y^{\prime }+9 y = 2 \,{\mathrm e}^{-x} \sin \left (x \right ) \]

22030

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

22031

\[ {} y^{\prime \prime }+9 y = 5 \cos \left (2 t \right ) \]

22032

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

22036

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

22037

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

22039

\[ {} y^{\prime \prime }-2 y^{\prime }-3 y+8 \,{\mathrm e}^{-x}+3 x = 0 \]

22049

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

22050

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

22061

\[ {} y^{\prime \prime }+4 y = 2 t -8 \]

22063

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

22079

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

22087

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

22245

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

22246

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

22247

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

22249

\[ {} y^{\prime \prime } = 9 x^{2}+2 x -1 \]

22254

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

22255

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

22256

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

22257

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

22258

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

22264

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