Internal problem ID [15324]
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. Superposition principle. Exercises page 137
Problem number: 555.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime }-y^{\prime \prime }=1+{\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve(diff(y(x),x$3)-diff(y(x),x$2)=1+exp(x),y(x), singsol=all)
\[ y \left (x \right ) = \left (c_{1} +x -2\right ) {\mathrm e}^{x}-\frac {x^{2}}{2}+c_{2} x +c_{3} \]
✓ Solution by Mathematica
Time used: 0.115 (sec). Leaf size: 28
DSolve[y'''[x]-y''[x]==1+Exp[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {x^2}{2}+c_3 x+e^x (x-2+c_1)+c_2 \]