8.11.4 problem 4

Internal problem ID [872]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number : 4
Date solved : Monday, January 27, 2025 at 03:11:01 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} 4 y^{\prime \prime }+4 y^{\prime }+y&=3 x \,{\mathrm e}^{x} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 24

dsolve(4*diff(y(x),x$2)+4*diff(y(x),x)+y(x)=3*x*exp(x),y(x), singsol=all)
 

\[ y = \left (c_1 x +c_2 \right ) {\mathrm e}^{-\frac {x}{2}}+\frac {\left (3 x -4\right ) {\mathrm e}^{x}}{9} \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 33

DSolve[4*D[y[x],{x,2}]+4*D[y[x],x]+y[x]==3*x*Exp[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{9} e^x (3 x-4)+e^{-x/2} (c_2 x+c_1) \]