4.2.76 Problems 7501 to 7600

Table 4.357: Second order linear ODE

#

ODE

Mathematica

Maple

Sympy

24742

\[ {} y^{\prime \prime }-4 y^{\prime }+4 y = 4-8 x +6 x \,{\mathrm e}^{2 x} \]

24743

\[ {} y^{\prime \prime }-9 y = 18 x -162 x \,{\mathrm e}^{2 x} \]

24744

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

24745

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

24746

\[ {} y^{\prime \prime }-4 y = 16 x \,{\mathrm e}^{-2 x}+8 x +4 \]

24747

\[ {} y^{\prime \prime }-4 y = 8 x \,{\mathrm e}^{2 x} \]

24748

\[ {} y^{\prime \prime }-9 y = -72 x \,{\mathrm e}^{-3 x} \]

24751

\[ {} y^{\prime \prime }+2 y^{\prime }+y = 48 \,{\mathrm e}^{-x} \cos \left (4 x \right ) \]

24752

\[ {} y^{\prime \prime }+4 y^{\prime }+4 y = 18 \,{\mathrm e}^{-2 x} \cos \left (3 x \right ) \]

24753

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

24754

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

24755

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

24756

\[ {} y^{\prime \prime }+7 y^{\prime }+12 y = {\mathrm e}^{-3 x} \sec \left (x \right )^{2} \left (1+2 \tan \left (x \right )\right ) \]

24757

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

24758

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

24759

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

24760

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

24761

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

24762

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

24763

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

24764

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

24767

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

24768

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

24769

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

24770

\[ {} y^{\prime \prime }+36 y = \sin \left (6 x \right ) \]

24771

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

24772

\[ {} y^{\prime \prime }+36 y = \cos \left (6 x \right ) \]

24773

\[ {} y^{\prime \prime }+3 y^{\prime }-4 y = 12 \,{\mathrm e}^{2 x} \]

24774

\[ {} y^{\prime \prime }+3 y^{\prime }-4 y = 21 \,{\mathrm e}^{3 x} \]

24775

\[ {} y^{\prime \prime }+3 y^{\prime }-4 y = 15 \,{\mathrm e}^{x} \]

24776

\[ {} y^{\prime \prime }+3 y^{\prime }-4 y = 20 \,{\mathrm e}^{-4 x} \]

24777

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

24778

\[ {} 4 y^{\prime \prime }-y = {\mathrm e}^{\frac {x}{2}}+12 \,{\mathrm e}^{x} \]

24781

\[ {} y^{\prime \prime }+16 y = 14 \cos \left (3 x \right ) \]

24782

\[ {} 4 y^{\prime \prime }+y = 33 \sin \left (3 x \right ) \]

24783

\[ {} y^{\prime \prime }+16 y = 24 \sin \left (4 x \right ) \]

24784

\[ {} y^{\prime \prime }+16 y = 48 \cos \left (4 x \right ) \]

24785

\[ {} y^{\prime \prime }+y = 12 \cos \left (2 x \right )-\sin \left (3 x \right ) \]

24786

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

24787

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

24788

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

24789

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

24790

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

24791

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

24792

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

24793

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

24794

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

24795

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

24796

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

24801

\[ {} y^{\prime \prime }-3 y^{\prime }+2 y = 6 x^{2}-6 x -11 \]

24802

\[ {} y^{\prime \prime }-3 y^{\prime }+2 y = 2 x^{3}-9 x^{2}+2 x -16 \]

24805

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

24806

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

24807

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

24809

\[ {} y^{\prime \prime }+4 y = 8 x^{5} \]

24810

\[ {} y^{\prime \prime }+4 y = 16 x \,{\mathrm e}^{2 x} \]

24811

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

24812

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

24813

\[ {} y^{\prime \prime }-4 y^{\prime }+13 y = 24 \,{\mathrm e}^{2 x} \sin \left (3 x \right ) \]

24814

\[ {} y^{\prime \prime }-4 y^{\prime }+13 y = 24 \,{\mathrm e}^{2 x} \sin \left (x \right ) \]

24815

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

24816

\[ {} y^{\prime \prime }-3 y^{\prime }+2 y = 72 x \,{\mathrm e}^{-x} \]

24817

\[ {} y^{\prime \prime }+4 y = 12 \sin \left (x \right )+12 \sin \left (2 x \right ) \]

24818

\[ {} y^{\prime \prime }+4 y = 20 \,{\mathrm e}^{x}-20 \cos \left (2 x \right ) \]

24819

\[ {} y^{\prime \prime }+16 y = 8 x +8 \sin \left (4 x \right ) \]

24820

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

24821

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

24823

\[ {} y^{\prime \prime }-4 y^{\prime }+13 y = 24 \,{\mathrm e}^{2 x} \cos \left (x \right ) \]

24824

\[ {} y^{\prime \prime }-4 y^{\prime }+13 y = 24 \,{\mathrm e}^{2 x} \cos \left (3 x \right ) \]

24825

\[ {} y^{\prime \prime }+25 y = \sin \left (5 x \right ) \]

24828

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

24829

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

24830

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

24831

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

24832

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

24833

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

24834

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

24835

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

24836

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

24837

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

24838

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

24839

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

24840

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

24841

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

24842

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

24843

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

24844

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

24845

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

24846

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

24847

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

24848

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

24849

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

24850

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

24851

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

24852

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

24853

\[ {} y^{\prime \prime }-5 y^{\prime }+4 y = \frac {6}{1+{\mathrm e}^{-2 x}} \]

24854

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

24855

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

24856

\[ {} y^{\prime \prime }-3 y^{\prime }+2 y = 15 \sqrt {1+{\mathrm e}^{-x}} \]

24857

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