4.23.3 Problems 201 to 300

Table 4.1341: Higher order, Linear, non-homogeneous and constant coefficients

#

ODE

Mathematica

Maple

Sympy

6626

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

6627

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

6637

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

6639

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

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

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

6646

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

6647

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

6650

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

6653

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

6654

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

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

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

6660

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

6662

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

6665

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

6667

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

6679

\[ {} 18 \,{\mathrm e}^{x}-3 y-11 y^{\prime }-8 y^{\prime \prime }+4 y^{\prime \prime \prime } = 0 \]

6736

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

6737

\[ {} 4 \,{\mathrm e}^{-x} \cos \left (x \right )+y^{\prime \prime \prime \prime } = 0 \]

6738

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

6739

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

6741

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

6745

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

6746

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

6747

\[ {} y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime } = 24 x \sin \left (x \right ) \]

6748

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

6755

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

6759

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

6770

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

6794

\[ {} y^{\prime }+2 y^{\prime \prime \prime }+y^{\left (5\right )} = a x +b \cos \left (x \right )+c \sin \left (x \right ) \]

7799

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = 2 x \,{\mathrm e}^{-x} \]

7813

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

7814

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

7815

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

7821

\[ {} y^{\prime \prime \prime \prime } = 5 x \]

7841

\[ {} y^{\prime \prime \prime }-y = 5 \]

7843

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

8000

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

8001

\[ {} y^{\left (5\right )}-4 y^{\prime \prime \prime } = 5 \]

8002

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

8019

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

8021

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

8025

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

8026

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

8029

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

8061

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

8815

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

8816

\[ {} y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+y = 3 \sin \left (t \right )-5 \cos \left (t \right ) \]

8817

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

8820

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

8825

\[ {} y^{\prime \prime \prime }+6 y^{\prime \prime }+11 y^{\prime }+6 y = 2 \sin \left (3 x \right ) \]

8868

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

8945

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

8946

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

8947

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

8948

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

8949

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

8958

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

8959

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

9270

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

9318

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

9319

\[ {} y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime } = 10+42 \,{\mathrm e}^{3 x} \]

9320

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

9618

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

9619

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

10158

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

10465

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

12727

\[ {} y^{\prime \prime \prime }-a^{2} y^{\prime }-{\mathrm e}^{2 a x} \sin \left (x \right )^{2} = 0 \]

12734

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

12735

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

12742

\[ {} 18 \,{\mathrm e}^{x}-3 y-11 y^{\prime }-8 y^{\prime \prime }+4 y^{\prime \prime \prime } = 0 \]

12798

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

12800

\[ {} y^{\prime \prime \prime \prime }-12 y^{\prime \prime }+12 y-16 x^{4} {\mathrm e}^{x^{2}} = 0 \]

12801

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

12805

\[ {} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+4 y-32 \sin \left (2 x \right )+24 \cos \left (2 x \right ) = 0 \]

12807

\[ {} 4 y^{\prime \prime \prime \prime }-12 y^{\prime \prime \prime }+11 y^{\prime \prime }-3 y^{\prime }-4 \cos \left (x \right ) = 0 \]

12838

\[ {} y^{\left (5\right )}+2 y^{\prime \prime \prime }+y^{\prime }-a x -b \sin \left (x \right )-c \cos \left (x \right ) = 0 \]

12839

\[ {} y^{\left (6\right )}+y-\sin \left (\frac {3 x}{2}\right ) \sin \left (\frac {x}{2}\right ) = 0 \]

12842

\[ {} y^{\left (5\right )}+a y^{\prime \prime \prime \prime }-f = 0 \]

14210

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

14212

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

14215

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

14217

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

14224

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

14225

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

14226

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

14228

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

14234

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

14236

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

14237

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

14239

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

14242

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

14245

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

14459

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

14462

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

14740

\[ {} y^{\prime \prime \prime }+4 y^{\prime \prime }+y^{\prime }-6 y = -18 x^{2}+1 \]

14741

\[ {} y^{\prime \prime \prime }+2 y^{\prime \prime }-3 y^{\prime }-10 y = 8 x \,{\mathrm e}^{-2 x} \]