4.27.25 Problems 2401 to 2500

Table 4.1601: Second order, Linear, non-homogeneous and constant coefficients

#

ODE

Mathematica

Maple

Sympy

24178

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

24179

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

24183

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

24184

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

24186

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

24187

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

24188

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

24189

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

24191

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

24635

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

24636

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

24638

\[ {} y^{\prime \prime }+4 y^{\prime }-5 y = 20 \]

24651

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

24652

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

24653

\[ {} y^{\prime \prime }-2 y^{\prime }-3 y = 27 x^{2} \]

24654

\[ {} y^{\prime \prime }-2 y^{\prime }-3 y = -6 x^{2}-8 x +4 \]

24655

\[ {} y^{\prime \prime }+4 y = 15 \,{\mathrm e}^{x}-8 x \]

24656

\[ {} y^{\prime \prime }+4 y = 15 \,{\mathrm e}^{x}-8 x^{2} \]

24657

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

24658

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

24659

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

24660

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

24661

\[ {} y^{\prime \prime }-4 y^{\prime }+3 y = 20 \cos \left (x \right ) \]

24662

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

24663

\[ {} y+2 y^{\prime }+y^{\prime \prime } = 7+75 \sin \left (2 x \right ) \]

24664

\[ {} 5 y+4 y^{\prime }+y^{\prime \prime } = 50 x +13 \,{\mathrm e}^{3 x} \]

24665

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

24666

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

24667

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

24668

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

24674

\[ {} -y+y^{\prime \prime } = 10 \sin \left (x \right )^{2} \]

24675

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

24676

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

24677

\[ {} y^{\prime \prime }+y = 10 \,{\mathrm e}^{2 x} \]

24678

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

24679

\[ {} y^{\prime \prime }+3 y^{\prime } = -18 x \]

24680

\[ {} 5 y+4 y^{\prime }+y^{\prime \prime } = 10 \,{\mathrm e}^{-3 x} \]

24681

\[ {} x^{\prime \prime }+4 x^{\prime }+5 x = 10 \]

24682

\[ {} x^{\prime \prime }+4 x^{\prime }+5 x = 8 \sin \left (t \right ) \]

24683

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

24684

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

24685

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

24686

\[ {} 2 y^{\prime \prime }-5 y^{\prime }-3 y = -9 x^{2}-1 \]

24687

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

24688

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

24689

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

24691

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

24692

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

24693

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

24694

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

24695

\[ {} y^{\prime \prime }+9 y = 4 \cos \left (x \right ) \]

24696

\[ {} y^{\prime \prime }+9 y = 15 \cos \left (2 x \right ) \]

24697

\[ {} y^{\prime \prime }+9 y = 18 x -3+20 \,{\mathrm e}^{x} \]

24698

\[ {} y^{\prime \prime }-y^{\prime } = 42 \,{\mathrm e}^{4 x} \]

24699

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

24700

\[ {} y^{\prime \prime }+6 y^{\prime }+14 y = 42 \,{\mathrm e}^{x}-7 \]

24701

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

24702

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

24703

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

24704

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

24705

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

24706

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

24707

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

24708

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

24709

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

24710

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

24711

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

24712

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

24713

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

24714

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

24715

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

24716

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

24717

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

24718

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

24719

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

24720

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

24721

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

24722

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

24729

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

24730

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

24731

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

24732

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

24739

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

24740

\[ {} y^{\prime \prime }-y^{\prime }-2 y = 36 x \,{\mathrm e}^{2 x} \]

24741

\[ {} 4 y-4 y^{\prime }+y^{\prime \prime } = 20-3 x \,{\mathrm e}^{2 x} \]

24742

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

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

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

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

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

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

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

24758

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