Internal problem ID [15342]
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: 573.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+3 y^{\prime }+2 y=6 x \,{\mathrm e}^{-x} \left (1-{\mathrm e}^{-x}\right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 36
dsolve(diff(y(x),x$2)+3*diff(y(x),x)+2*y(x)=6*x*exp(-x)*(1-exp(-x)),y(x), singsol=all)
\[ y \left (x \right ) = 3 \left (\left (x^{2}+2 x -\frac {1}{3} c_{1} +2\right ) {\mathrm e}^{-x}+x^{2}-2 x +\frac {c_{2}}{3}\right ) {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.186 (sec). Leaf size: 39
DSolve[y''[x]+3*y'[x]+2*y[x]==6*x*Exp[-x]*(1-Exp[-x]),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-2 x} \left (3 x^2+e^x \left (3 x^2-6 x+6+c_2\right )+6 x+6+c_1\right ) \]