4.20.13 Problems 1201 to 1300

Table 4.1223: Second or higher order ODE with constant coefficients

#

ODE

Mathematica

Maple

Sympy

5780

\[ {} y^{\prime \prime }-2 y^{\prime }+y = 50 \cosh \left (x \right ) \cos \left (x \right ) \]

5781

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

5782

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

5783

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

5784

\[ {} y^{\prime \prime }+2 y^{\prime }+5 y = 8 \sinh \left (x \right ) \]

5785

\[ {} \csc \left (a \right )^{2} y-2 \tan \left (a \right ) y^{\prime }+y^{\prime \prime } = 0 \]

5786

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

5787

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

5788

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

5789

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

5790

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

5791

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

5792

\[ {} -4 y-3 y^{\prime }+y^{\prime \prime } = 0 \]

5793

\[ {} -4 y-3 y^{\prime }+y^{\prime \prime } = 10 \cos \left (2 x \right ) \]

5794

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

5795

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

5796

\[ {} 5 y+4 y^{\prime }+y^{\prime \prime } = 0 \]

5797

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

5798

\[ {} y^{\prime \prime }-4 y^{\prime }+13 y = 0 \]

5799

\[ {} 6 y-5 y^{\prime }+y^{\prime \prime } = 0 \]

5800

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

5801

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

5802

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

5803

\[ {} y^{\prime \prime }+6 y^{\prime }+9 y = \cosh \left (x \right ) {\mathrm e}^{-3 x} \]

5804

\[ {} 12 y-7 y^{\prime }+y^{\prime \prime } = 0 \]

5805

\[ {} 12 y-7 y^{\prime }+y^{\prime \prime } = x \]

5806

\[ {} 16 y+8 y^{\prime }+y^{\prime \prime } = 0 \]

5807

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

5808

\[ {} 20 y-9 y^{\prime }+y^{\prime \prime } = 0 \]

5809

\[ {} 20 y-9 y^{\prime }+y^{\prime \prime } = x^{2} {\mathrm e}^{3 x} \]

5810

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

5811

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

5812

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

5813

\[ {} \left (a^{2}+b^{2}\right )^{2} y-4 a b y^{\prime }+y^{\prime \prime } = 0 \]

5814

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

5815

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

5887

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

5890

\[ {} 3 y-8 y^{\prime }+4 y^{\prime \prime } = 0 \]

5951

\[ {} y+2 y^{\prime }+4 y^{\prime \prime } = 0 \]

5952

\[ {} -y-2 y^{\prime }+4 y^{\prime \prime } = 0 \]

6303

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

6304

\[ {} y^{\prime \prime } = a y \]

6610

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

6611

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

6612

\[ {} \sin \left (x \right )+y^{\prime \prime \prime } = 0 \]

6613

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

6614

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

6615

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

6616

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

6617

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

6619

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

6620

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

6621

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

6622

\[ {} 4 y-2 y^{\prime }+y^{\prime \prime \prime } = 0 \]

6623

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

6624

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

6625

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

6626

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

6627

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

6628

\[ {} y^{\prime \prime \prime }-7 y^{\prime }+6 y = 0 \]

6629

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

6633

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

6634

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

6635

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

6636

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

6637

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

6638

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

6639

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

6640

\[ {} -15 y-7 y^{\prime }+y^{\prime \prime }+y^{\prime \prime \prime } = 0 \]

6641

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

6642

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

6643

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

6644

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

6645

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

6646

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

6647

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

6648

\[ {} 10 y+3 y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime } = 0 \]

6649

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

6650

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

6651

\[ {} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y = 0 \]

6652

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

6653

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

6654

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

6655

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

6656

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

6657

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

6658

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

6659

\[ {} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-2 y = 0 \]

6660

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

6661

\[ {} y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y = 0 \]

6662

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

6663

\[ {} -4 y+6 y^{\prime }-4 y^{\prime \prime }+y^{\prime \prime \prime } = 0 \]

6664

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

6665

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y = x^{2} {\mathrm e}^{2 x} \]

6666

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

6667

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

6668

\[ {} y^{\prime \prime \prime } = a y^{\prime \prime } \]

6669

\[ {} \operatorname {a3} y+\operatorname {a2} y^{\prime }+\operatorname {a1} y^{\prime \prime }+y^{\prime \prime \prime } = 0 \]

6677

\[ {} 4 y^{\prime \prime \prime }-3 y^{\prime }+y = 0 \]

6678

\[ {} -3 y-11 y^{\prime }-8 y^{\prime \prime }+4 y^{\prime \prime \prime } = 0 \]