Internal problem ID [15331]
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: 562.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }+2 y=\left (5 x +4\right ) {\mathrm e}^{x}+{\mathrm e}^{-x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
dsolve(diff(y(x),x$2)+2*diff(y(x),x)+2*y(x)=(5*x+4)*exp(x)+exp(-x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-x} \sin \left (x \right ) c_{2} +{\mathrm e}^{-x} \cos \left (x \right ) c_{1} +{\mathrm e}^{x} x +{\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.193 (sec). Leaf size: 30
DSolve[y''[x]+2*y'[x]+2*y[x]==(5*x+4)*Exp[x]+Exp[-x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x} \left (e^{2 x} x+c_2 \cos (x)+c_1 \sin (x)+1\right ) \]