Internal problem ID [15328]
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: 559.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-y^{\prime }-2 y=4 x -2 \,{\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(diff(y(x),x$2)-diff(y(x),x)-2*y(x)=4*x-2*exp(x),y(x), singsol=all)
\[ y \left (x \right ) = c_{2} {\mathrm e}^{-x}+c_{1} {\mathrm e}^{2 x}+{\mathrm e}^{x}-2 x +1 \]
✓ Solution by Mathematica
Time used: 0.111 (sec). Leaf size: 29
DSolve[y''[x]-y'[x]-2*y[x]==4*x-2*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -2 x+e^x+c_1 e^{-x}+c_2 e^{2 x}+1 \]