4.27.19 Problems 1801 to 1900

Table 4.1589: Second order, Linear, non-homogeneous and constant coefficients

#

ODE

Mathematica

Maple

Sympy

19072

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

19073

\[ {} y^{\prime \prime }+3 y^{\prime }+2 y = \cos \left (\alpha t \right ) \]

19076

\[ {} \frac {7 y^{\prime \prime }}{5}+y = \operatorname {Heaviside}\left (t \right ) \]

19077

\[ {} \frac {8 y^{\prime \prime }}{5}+y = \operatorname {Heaviside}\left (t \right ) \]

19179

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

19302

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

19303

\[ {} y^{\prime \prime }-6 y^{\prime }+8 y = {\mathrm e}^{x}+{\mathrm e}^{2 x} \]

19306

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

19307

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

19308

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

19309

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

19310

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

19311

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

19537

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

19539

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

19540

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

19541

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

19542

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

19543

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

19545

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

19609

\[ {} y^{\prime \prime }+3 y^{\prime }-10 y = 6 \,{\mathrm e}^{4 x} \]

19610

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

19611

\[ {} y^{\prime \prime }+10 y^{\prime }+25 y = 14 \,{\mathrm e}^{-5 x} \]

19612

\[ {} y^{\prime \prime }-2 y^{\prime }+5 y = 25 x^{2}+12 \]

19613

\[ {} y^{\prime \prime }-y^{\prime }-6 y = 20 \,{\mathrm e}^{-2 x} \]

19614

\[ {} y^{\prime \prime }-3 y^{\prime }+2 y = 14 \sin \left (2 x \right )-18 \cos \left (2 x \right ) \]

19615

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

19616

\[ {} y^{\prime \prime }-2 y^{\prime } = 12 x -10 \]

19617

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

19618

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

19619

\[ {} y^{\prime \prime }+y^{\prime } = 10 x^{4}+2 \]

19620

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

19621

\[ {} y^{\prime \prime }+4 y = 4 \cos \left (2 x \right )+6 \cos \left (x \right )+8 x^{2}-4 x \]

19622

\[ {} y^{\prime \prime }+9 y = 2 \sin \left (3 x \right )+4 \sin \left (x \right )-26 \,{\mathrm e}^{-2 x}+27 x^{3} \]

19623

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

19624

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

19625

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

19626

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

19627

\[ {} y^{\prime \prime }-2 y^{\prime }-3 y = 64 x \,{\mathrm e}^{-x} \]

19628

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

19629

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

19630

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

19631

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

19632

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

19633

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

19634

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

19635

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

19636

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

19637

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

19666

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

19667

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

19668

\[ {} y^{\prime \prime }+4 y^{\prime }+4 y = 10 x^{3} {\mathrm e}^{-2 x} \]

19669

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

19670

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

19671

\[ {} y^{\prime \prime }-2 y^{\prime }-3 y = 6 \,{\mathrm e}^{5 x} \]

19672

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

19674

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

19677

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

19678

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

19681

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

19682

\[ {} 12 y-7 y^{\prime }+y^{\prime \prime } = {\mathrm e}^{2 x} \left (x^{3}-5 x^{2}\right ) \]

19683

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

19692

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

19740

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

19741

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

19742

\[ {} y^{\prime \prime }+2 y^{\prime }+5 y = 3 \,{\mathrm e}^{-x} \sin \left (x \right ) \]

19747

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

19748

\[ {} y^{\prime \prime }+5 y^{\prime }+6 y = 4 \,{\mathrm e}^{3 t} \]

19749

\[ {} y^{\prime \prime }+y^{\prime }-6 y = t \]

19750

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

19751

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

19811

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

19812

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

19813

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

19814

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

19815

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

19816

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

19871

\[ {} v^{\prime \prime }-6 v^{\prime }+13 v = {\mathrm e}^{-2 u} \]

19872

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

19873

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

19893

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

19949

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

19951

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

19952

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

19955

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

19956

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

19957

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

19959

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

19963

\[ {} e y^{\prime \prime } = \frac {P \left (\frac {L}{2}-x \right )}{2} \]

19964

\[ {} e y^{\prime \prime } = \frac {w \left (\frac {L^{2}}{4}-x^{2}\right )}{2} \]

19965

\[ {} e y^{\prime \prime } = -\frac {\left (w L +P \right ) x}{2}-\frac {w \,x^{2}}{2} \]

19966

\[ {} e y^{\prime \prime } = -P \left (L -x \right ) \]

19967

\[ {} e y^{\prime \prime } = -P L +\left (w L +P \right ) x -\frac {w \left (L^{2}+x^{2}\right )}{2} \]

19983

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

19991

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

20161

\[ {} 6 y-5 y^{\prime }+y^{\prime \prime } = {\mathrm e}^{4 x} \]

20162

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

20163

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

20167

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

20171

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