Internal problem ID [15268]
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: 498.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+4 y^{\prime \prime }=1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve(diff(y(x),x$4)+4*diff(y(x),x$3)+4*diff(y(x),x$2)=1,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (2 c_{1} x +2 c_{1} +2 c_{2} \right ) {\mathrm e}^{-2 x}}{8}+\frac {x^{2}}{8}+c_{3} x +c_{4} \]
✓ Solution by Mathematica
Time used: 0.166 (sec). Leaf size: 37
DSolve[y''''[x]+4*y'''[x]+4*y''[x]==1,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x^2}{8}+c_4 x+\frac {1}{4} e^{-2 x} (c_2 (x+1)+c_1)+c_3 \]