75.16.48 problem 521

Internal problem ID [17021]
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 ODEs). Section 15.3 Nonhomogeneous linear equations with constant coefficients. Trial and error method. Exercises page 132
Problem number : 521
Date solved : Tuesday, January 28, 2025 at 09:45:43 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=8 \,{\mathrm e}^{-2 x} \end{align*}

Solution by Maple

Time used: 0.004 (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)
 
\[ y = {\mathrm e}^{-2 x} \left (c_{1} x +4 x^{2}+c_{2} \right ) \]

Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 23

DSolve[D[y[x],{x,2}]+4*D[y[x],x]+4*y[x]==8*Exp[-2*x],y[x],x,IncludeSingularSolutions -> True]
 
\[ y(x)\to e^{-2 x} \left (4 x^2+c_2 x+c_1\right ) \]