Internal problem ID [15358]
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: 589.
ODE order: 5.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_y]]
\[ \boxed {y^{\left (5\right )}-y^{\prime \prime \prime }=x +2 \,{\mathrm e}^{-x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 38
dsolve(diff(y(x),x$5)-diff(y(x),x$3)=x+2*exp(-x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (7+2 x -2 c_{1} \right ) {\mathrm e}^{-x}}{2}-\frac {x^{4}}{24}+\frac {c_{3} x^{2}}{2}+c_{4} x +c_{2} {\mathrm e}^{x}+c_{5} \]
✓ Solution by Mathematica
Time used: 0.394 (sec). Leaf size: 46
DSolve[y'''''[x]-y'''[x]==x+2*Exp[-x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {x^4}{24}+c_5 x^2+c_4 x+c_1 e^x+e^{-x} \left (x+\frac {7}{2}-c_2\right )+c_3 \]