Internal problem ID [15267]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 15.3 Nonhomogeneous linear equations with
constant coefficients. Trial and error method. Exercises page 132
Problem number: 497.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }=4} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 24
dsolve(diff(y(x),x$4)-diff(y(x),x$3)=4,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{x}+\frac {c_{2} x^{2}}{2}-\frac {2 x^{3}}{3}+c_{3} x +c_{4} \]
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 31
DSolve[y''''[x]-y'''[x]==4,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {2 x^3}{3}+c_4 x^2+c_3 x+c_1 e^x+c_2 \]