Internal problem ID [15271]
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: 501.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+y^{\prime \prime }=x \,{\mathrm e}^{-x}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 37
dsolve(diff(y(x),x$4)+2*diff(y(x),x$3)+diff(y(x),x$2)=x*exp(-x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (24+x^{3}+6 x^{2}+6 \left (3+c_{1} \right ) x +12 c_{1} +6 c_{2} \right ) {\mathrm e}^{-x}}{6}+c_{3} x +c_{4} \]
✓ Solution by Mathematica
Time used: 0.127 (sec). Leaf size: 52
DSolve[y''''[x]+2*y'''[x]+y''[x]==x*Exp[-x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{6} e^{-x} \left (x^3+6 x^2+6 x \left (c_4 e^x+3+c_2\right )+6 \left (c_3 e^x+4+c_1+2 c_2\right )\right ) \]