Internal problem ID [15320]
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: 551.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-y^{\prime }-2 y={\mathrm e}^{x}+{\mathrm e}^{-2 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 30
dsolve(diff(y(x),x$2)-diff(y(x),x)-2*y(x)=exp(x)+exp(-2*x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (4 c_{1} {\mathrm e}^{4 x}-2 \,{\mathrm e}^{3 x}+4 c_{2} {\mathrm e}^{x}+1\right ) {\mathrm e}^{-2 x}}{4} \]
✓ Solution by Mathematica
Time used: 0.114 (sec). Leaf size: 39
DSolve[y''[x]-y'[x]-2*y[x]==Exp[x]+Exp[-2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{4} e^{-2 x} \left (-2 e^{3 x}+4 c_1 e^x+4 c_2 e^{4 x}+1\right ) \]