Internal problem ID [15291]
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: 521.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+4 y^{\prime }+4 y=8 \,{\mathrm e}^{-2 x}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 19
dsolve(diff(y(x),x$2)+4*diff(y(x),x)+4*y(x)=8*exp(-2*x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-2 x} \left (c_{1} x +4 x^{2}+c_{2} \right ) \]
✓ Solution by Mathematica
Time used: 0.025 (sec). Leaf size: 23
DSolve[y''[x]+4*y'[x]+4*y[x]==8*Exp[-2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-2 x} \left (4 x^2+c_2 x+c_1\right ) \]