6.68 Problems 6701 to 6800

Table 6.135: Main lookup table sequentially arranged

#

ODE

Mathematica

Maple

Sympy

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

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

6703

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

6704

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

6705

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

6706

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

6707

\[ {} -8 y+3 x y^{\prime }+x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime } = 0 \]

6708

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

6709

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

6710

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

6711

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

6712

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

6713

\[ {} -8 y+7 x y^{\prime }-3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime } = 0 \]

6714

\[ {} \left (-a^{2}+1\right ) x y^{\prime }+3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime } = 0 \]

6715

\[ {} 8 y-8 x y^{\prime }+4 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime } = 0 \]

6716

\[ {} -2 \left (x^{2}+4\right ) y+x \left (x^{2}+8\right ) y^{\prime }-4 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime } = 0 \]

6717

\[ {} -\left (-a \,x^{3}+12\right ) y+6 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime } = 0 \]

6718

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

6719

\[ {} 6 y+18 x y^{\prime }+9 x^{2} y^{\prime \prime }+\left (x^{3}+1\right ) y^{\prime \prime \prime } = 0 \]

6720

\[ {} -12 y+3 \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (x^{2}+1\right ) y^{\prime \prime \prime } = 0 \]

6721

\[ {} -4 y-14 x y^{\prime }+\left (-8 x^{2}+3\right ) y^{\prime \prime }+x \left (-x^{2}+1\right ) y^{\prime \prime \prime } = 0 \]

6722

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

6723

\[ {} -8 y+3 y^{\prime } \left (1+x \right )+\left (1+x \right )^{2} y^{\prime \prime }+\left (1+x \right )^{3} y^{\prime \prime \prime } = 0 \]

6724

\[ {} -6 y+6 y^{\prime } \left (1+x \right )-3 x \left (x +2\right ) y^{\prime \prime }+x^{2} \left (3+y\right ) y^{\prime \prime \prime } = 0 \]

6725

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

6726

\[ {} 2 y+\left (1-2 x \right ) y^{\prime }+\left (1-2 x \right )^{3} y^{\prime \prime \prime } = 0 \]

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

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

6730

\[ {} -4 \left (3 x +1\right ) y+2 x \left (5 x +2\right ) y^{\prime }-2 x^{2} \left (2 x +1\right ) y^{\prime \prime }+x^{3} \left (1+x \right ) y^{\prime \prime \prime } = 0 \]

6731

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

6732

\[ {} -4 \left (3 x^{2}+1\right ) y+2 x \left (5 x^{2}+2\right ) y^{\prime }-2 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x^{3} \left (x^{2}+1\right ) y^{\prime \prime \prime } = 0 \]

6733

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

6734

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

6735

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

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

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

6740

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

6741

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

6742

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

6743

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

6744

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

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

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

6749

\[ {} -8 y-2 y^{\prime \prime }+y^{\prime \prime \prime \prime } = 0 \]

6750

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

6751

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

6752

\[ {} 27 y-12 y^{\prime \prime }+y^{\prime \prime \prime \prime } = 0 \]

6753

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

6754

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

6755

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

6756

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

6757

\[ {} 10 f^{\prime }\left (x \right ) y^{\prime }+3 y \left (3 f \left (x \right )^{2}+f^{\prime \prime }\left (x \right )\right )+10 f \left (x \right ) y^{\prime \prime }+y^{\prime \prime \prime \prime } = 0 \]

6758

\[ {} -2 y+5 y^{\prime }-3 y^{\prime \prime }-y^{\prime \prime \prime }+y^{\prime \prime \prime \prime } = 0 \]

6759

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

6760

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

6761

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

6762

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

6763

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

6764

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

6765

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

6766

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

6767

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

6768

\[ {} 16 y-16 y^{\prime }+12 y^{\prime \prime }-4 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime } = 0 \]

6769

\[ {} a^{4} x^{4} y+4 a^{3} x^{3} y^{\prime }+6 a^{2} x^{2} y^{\prime \prime }+4 a x y^{\prime \prime \prime }+y^{\prime \prime \prime \prime } = 0 \]

6770

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

6771

\[ {} -3 y^{\prime }+11 y^{\prime \prime }-12 y^{\prime \prime \prime }+4 y^{\prime \prime \prime \prime } = 0 \]

6772

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

6773

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

6774

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

6775

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

6776

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

6777

\[ {} 6 y^{\prime \prime }+6 x y^{\prime \prime \prime }+x^{2} y^{\prime \prime \prime \prime } = 0 \]

6778

\[ {} 12 y^{\prime \prime }+8 x y^{\prime \prime \prime }+x^{2} y^{\prime \prime \prime \prime } = 0 \]

6779

\[ {} -a^{2} y+12 y^{\prime \prime }+8 x y^{\prime \prime \prime }+x^{2} y^{\prime \prime \prime \prime } = 0 \]

6780

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

6781

\[ {} -c^{4} y+16 \left (1+a -b \right ) \left (2+a -b \right ) y^{\prime \prime }+32 \left (2+a -b \right ) x y^{\prime \prime \prime }+16 x^{2} y^{\prime \prime \prime \prime } = 0 \]

6782

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

6783

\[ {} 6 x y^{\prime \prime }+6 x^{2} y^{\prime \prime \prime }+x^{3} y^{\prime \prime \prime \prime } = 0 \]

6784

\[ {} -k y-\left (-a b c +x \right ) y^{\prime }+\left (a b +a c +b c +a +b +c +1\right ) x y^{\prime \prime }+\left (3+a +b +c \right ) x^{2} y^{\prime \prime \prime }+x^{3} y^{\prime \prime \prime \prime } = 0 \]

6785

\[ {} -4 y-2 x y^{\prime }+4 x^{2} y^{\prime \prime }+6 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime } = 0 \]

6786

\[ {} y+3 x y^{\prime }+9 x^{2} y^{\prime \prime }+6 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime } = 0 \]

6787

\[ {} 12 x^{2} y^{\prime \prime }+8 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime } = 0 \]

6788

\[ {} a y+12 x^{2} y^{\prime \prime }+8 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime } = 0 \]

6789

\[ {} \operatorname {A4} y+\operatorname {A3} x y^{\prime }+\operatorname {A2} \,x^{2} y^{\prime \prime }+\operatorname {A1} \,x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime } = 0 \]

6790

\[ {} -b^{4} x^{\frac {2}{a}} y+16 \left (-2 a +1\right ) \left (1-a \right ) a^{2} x^{2} y^{\prime \prime }-32 \left (-2 a +1\right ) a^{2} x^{3} y^{\prime \prime \prime }+16 a^{4} x^{4} y^{\prime \prime \prime \prime } = 0 \]

6791

\[ {} y \,{\mathrm e}^{x}+4 \,{\mathrm e}^{x} y^{\prime }+6 \,{\mathrm e}^{x} y^{\prime \prime }+4 \left ({\mathrm e}^{x}+2\right ) y^{\prime \prime \prime }+\left ({\mathrm e}^{x}+2 x \right ) y^{\prime \prime \prime \prime } = 0 \]

6792

\[ {} 2 y^{\prime }-2 y^{\prime \prime }-y^{\prime \prime \prime }+y^{\left (5\right )} = 0 \]

6793

\[ {} y^{\prime }+2 y^{\prime \prime \prime }+y^{\left (5\right )} = 0 \]

6794

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

6795

\[ {} y^{\left (6\right )} = 0 \]

6796

\[ {} a y+y^{\left (6\right )} = 0 \]

6797

\[ {} y+2 y^{\prime \prime \prime }+y^{\left (6\right )} = 0 \]

6798

\[ {} y^{\left (8\right )} = y \]

6799

\[ {} y-2 y^{\prime \prime \prime \prime }+y^{\left (8\right )} = 0 \]

6800

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