4.2.75 Problems 7401 to 7500

Table 4.355: Second order linear ODE

#

ODE

Mathematica

Maple

Sympy

24547

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

24548

\[ {} y^{\prime \prime }-2 y^{\prime }+3 y = 0 \]

24549

\[ {} y^{\prime \prime }-y^{\prime }-6 y = 0 \]

24550

\[ {} y^{\prime \prime }-2 y^{\prime }-3 y = 0 \]

24552

\[ {} y^{\prime \prime }-y^{\prime }-6 y = 0 \]

24553

\[ {} y^{\prime \prime }+3 y^{\prime }-10 y = 0 \]

24555

\[ {} 4 y^{\prime \prime }-4 y^{\prime }+y = 0 \]

24556

\[ {} y^{\prime \prime }+6 y^{\prime }+9 y = 0 \]

24575

\[ {} y^{\prime \prime }+4 y^{\prime }+4 y = 0 \]

24576

\[ {} y^{\prime \prime }+4 y^{\prime }+4 y = 0 \]

24581

\[ {} 4 y^{\prime \prime }-4 y^{\prime }+y = 0 \]

24584

\[ {} y^{\prime \prime }+a^{2} y-2 a y^{\prime }+y b^{2} = 0 \]

24585

\[ {} y^{\prime \prime }-2 y^{\prime }+5 y = 0 \]

24586

\[ {} y^{\prime \prime }-2 y^{\prime }+2 y = 0 \]

24587

\[ {} y^{\prime \prime }+9 y = 0 \]

24588

\[ {} y^{\prime \prime }-9 y = 0 \]

24589

\[ {} y^{\prime \prime }+6 y^{\prime }+13 y = 0 \]

24590

\[ {} y^{\prime \prime }-4 y^{\prime }+7 y = 0 \]

24592

\[ {} y^{\prime \prime }-y = 0 \]

24593

\[ {} y^{\prime \prime }+y = 0 \]

24602

\[ {} x^{\prime \prime }+k^{2} x = 0 \]

24604

\[ {} x^{\prime \prime }+2 b x^{\prime }+k^{2} x = 0 \]

24617

\[ {} y^{\prime \prime }-y^{\prime }-6 y = 0 \]

24628

\[ {} y^{\prime \prime }+2 y^{\prime }+5 y = 0 \]

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

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

24664

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

24665

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

24666

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

24667

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

24668

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

24674

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

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

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

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

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

24684

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

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

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

24707

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

24708

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

24709

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

24710

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

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

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

24721

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

24722

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

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

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

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

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