Internal problem ID [15310]
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: 540.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y=x^{2}+x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve(diff(y(x),x$3)-diff(y(x),x$2)+diff(y(x),x)-y(x)=x+x^2,y(x), singsol=all)
\[ y \left (x \right ) = -x^{2}-3 x -1+\cos \left (x \right ) c_{1} +c_{2} {\mathrm e}^{x}+c_{3} \sin \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 31
DSolve[y'''[x]-y''[x]+y'[x]-y[x]==x+x^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -x^2-3 x+c_3 e^x+c_1 \cos (x)+c_2 \sin (x)-1 \]