4.12.7 Problems 601 to 700

Table 4.1091: Third and higher order linear ODE

#

ODE

Mathematica

Maple

Sympy

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

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

7056

\[ {} y^{\prime \prime \prime }+y^{\prime \prime }-10 y^{\prime }-6 y = 0 \]

7057

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

7058

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

7059

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

7062

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

7064

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

7065

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y = 0 \]

7067

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

7068

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

7069

\[ {} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-11 y^{\prime \prime }-12 y^{\prime }+36 y = 0 \]

7070

\[ {} 36 y^{\prime \prime \prime \prime }-37 y^{\prime \prime }+4 y^{\prime }+5 y = 0 \]

7071

\[ {} y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+36 y = 0 \]

7074

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

7076

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

7077

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

7078

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

7079

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

7084

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

7282

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

7283

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

7284

\[ {} y^{\prime \prime \prime }+3 y^{\prime \prime }-9 y^{\prime }-5 y = 0 \]

7285

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

7345

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

7364

\[ {} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+13 y^{\prime \prime }-18 y^{\prime }+36 y = 0 \]

7620

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

7621

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

7622

\[ {} z^{\prime \prime \prime }+2 z^{\prime \prime }-4 z^{\prime }-8 z = 0 \]

7623

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

7624

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

7625

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

7626

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

7627

\[ {} 3 y^{\prime \prime \prime }+18 y^{\prime \prime }+13 y^{\prime }-19 y = 0 \]

7628

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

7629

\[ {} y^{\left (5\right )}-3 y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+15 y^{\prime \prime }+4 y^{\prime }-12 y = 0 \]

7677

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

7679

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

7680

\[ {} x^{\prime \prime \prime }-3 x^{\prime \prime }-9 x^{\prime }-5 x = 0 \]

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

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

7842

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

7843

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

7979

\[ {} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y = 0 \]

7983

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

7989

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

7991

\[ {} y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+12 y^{\prime \prime }-8 y^{\prime } = 0 \]

7994

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

7995

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

7996

\[ {} y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+13 y^{\prime \prime }-12 y^{\prime }+4 y = 0 \]

7997

\[ {} y^{\left (6\right )}+9 y^{\prime \prime \prime \prime }+24 y^{\prime \prime }+16 y = 0 \]

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

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

8061

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

8065

\[ {} \left (2 x -3\right ) y^{\prime \prime \prime }-\left (6 x -7\right ) y^{\prime \prime }+4 x y^{\prime }-4 y = 8 \]

8066

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

8164

\[ {} t^{5} y^{\prime \prime \prime \prime }-t^{3} y^{\prime \prime }+6 y = 0 \]

8185

\[ {} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-x y^{\prime }+y = 12 x^{2} \]

8199

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

8217

\[ {} y^{\prime \prime \prime \prime }-20 y^{\prime \prime \prime }+158 y^{\prime \prime }-580 y^{\prime }+841 y = 0 \]

8218

\[ {} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+20 x y^{\prime }-78 y = 0 \]

8771

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

8774

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

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

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