Internal problem ID [5371]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 14. Linear equations with constant coefficients. Supplemetary problems. Page
92
Problem number: 14.
ODE order: 5.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\left (5\right )}-4 y^{\prime \prime \prime }=5} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 34
dsolve(diff(y(x),x$5)-4*diff(y(x),x$3)=5,y(x), singsol=all)
\[ y = -\frac {5 x^{3}}{24}+\frac {c_{1} {\mathrm e}^{2 x}}{8}+\frac {c_{3} x^{2}}{2}-\frac {{\mathrm e}^{-2 x} c_{2}}{8}+c_{4} x +c_{5} \]
✓ Solution by Mathematica
Time used: 0.079 (sec). Leaf size: 47
DSolve[y'''''[x]-4*y'''[x]==5,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {5 x^3}{24}+c_5 x^2+c_4 x+\frac {1}{8} c_1 e^{2 x}-\frac {1}{8} c_2 e^{-2 x}+c_3 \]