Internal problem ID [15357]
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: 588.
ODE order: 5.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_y]]
\[ \boxed {y^{\left (5\right )}-y^{\prime \prime \prime \prime }=x \,{\mathrm e}^{x}-1} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 41
dsolve(diff(y(x),x$5)-diff(y(x),x$4)=x*exp(x)-1,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (x^{2}+2 c_{1} -8 x +20\right ) {\mathrm e}^{x}}{2}+\frac {x^{4}}{24}+\frac {c_{2} x^{3}}{6}+\frac {c_{3} x^{2}}{2}+c_{4} x +c_{5} \]
✓ Solution by Mathematica
Time used: 0.337 (sec). Leaf size: 49
DSolve[y'''''[x]-y''''[x]==x*Exp[x]-1,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x^4}{24}+c_5 x^3+c_4 x^2+e^x \left (\frac {x^2}{2}-4 x+10+c_1\right )+c_3 x+c_2 \]