Internal problem ID [15283]
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: 513.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime }+y^{\prime \prime }=1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve(diff(y(x),x$3)+diff(y(x),x$2)=1,y(x), singsol=all)
\[ y \left (x \right ) = \frac {x^{2}}{2}+c_{1} {\mathrm e}^{-x}+c_{2} x +c_{3} \]
✓ Solution by Mathematica
Time used: 0.031 (sec). Leaf size: 27
DSolve[y'''[x]+y''[x]==1,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x^2}{2}+c_3 x+c_1 e^{-x}+c_2 \]