4.19.3 Problems 201 to 300

Table 4.1183: Third and higher order non-homogeneous ODE

#

ODE

Mathematica

Maple

Sympy

4477

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

4478

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

4489

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

4490

\[ {} y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y = 40 \sin \left (2 x \right ) \]

4491

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

4492

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = 10 \,{\mathrm e}^{x} \sin \left (x \right ) \]

4493

\[ {} y^{\prime \prime \prime }-2 y^{\prime }-4 y = 50 \,{\mathrm e}^{2 x}+50 \sin \left (x \right ) \]

4494

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

4495

\[ {} y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+16 y = 32 \,{\mathrm e}^{2 x}+16 x^{3} \]

4496

\[ {} y^{\prime \prime \prime \prime }-18 y^{\prime \prime }+81 y = 72 \,{\mathrm e}^{3 x}+729 x^{2} \]

4511

\[ {} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-x y^{\prime }+y = 9 x^{2} \ln \left (x \right ) \]

4513

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

4529

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

4530

\[ {} y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y = 120 \,{\mathrm e}^{3 t} \operatorname {Heaviside}\left (t -1\right ) \]

4531

\[ {} y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-4 y = 40 t^{2} \operatorname {Heaviside}\left (t -2\right ) \]

4532

\[ {} y^{\prime \prime \prime \prime }+4 y = \left (2 t^{2}+t +1\right ) \delta \left (t -1\right ) \]

6611

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

6612

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

6613

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

6615

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

6616

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

6621

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

6623

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

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

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

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

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

6673

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

6674

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

6679

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

6680

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

6684

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

6689

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

6690

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

6691

\[ {} 4 y^{\prime }+5 x y^{\prime \prime }+x^{2} y^{\prime \prime \prime } = \ln \left (x \right ) \]

6701

\[ {} y+x y^{\prime }+\left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime \prime }+x \left (\operatorname {b0} x +\operatorname {a0} \right ) y^{\prime \prime \prime } = f \left (x \right ) \]

6702

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

6704

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

6706

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

6711

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

6718

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

6727

\[ {} 2 x y+2 x^{3} y^{\prime \prime }+x^{4} y^{\prime \prime \prime } = 10 x^{2}+10 \]

6728

\[ {} x y-x^{2} y^{\prime }+2 x^{3} y^{\prime \prime }+x^{4} y^{\prime \prime \prime } = 1 \]

6729

\[ {} 10 x^{2} y^{\prime }+8 x^{3} y^{\prime \prime }+x^{2} \left (x^{2}+1\right ) y^{\prime \prime \prime } = -1+3 x^{2}+2 x^{2} \ln \left (x \right ) \]

6731

\[ {} 4 x^{2} y^{\prime }-4 x^{3} y^{\prime \prime }+4 x^{4} y^{\prime \prime \prime } = 1 \]

6734

\[ {} \sin \left (x \right )-y \cos \left (x \right )-3 y^{\prime } \sin \left (x \right )+3 \left (\cos \left (x \right )+1\right ) y^{\prime \prime }+\left (x +\sin \left (x \right )\right ) y^{\prime \prime \prime } = 0 \]

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

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

6761

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

6770

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

6780

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

6794

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

6803

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

6816

\[ {} {y^{\prime }}^{3} y^{\prime \prime \prime } = 1 \]

6817

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

6819

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

6820

\[ {} 1-{y^{\prime \prime }}^{2}+2 x y^{\prime \prime } y^{\prime \prime \prime }+\left (-x^{2}+1\right ) {y^{\prime \prime \prime }}^{2} = 0 \]

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

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

7983

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

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

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

8038

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

8039

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