50.14.22 problem 3(f)

Internal problem ID [8060]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 2. Problems for Review and Discovery. Drill excercises. Page 105
Problem number : 3(f)
Date solved : Monday, January 27, 2025 at 03:41:05 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+4 y^{\prime }+4 y&=x \ln \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 37

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

\[ y = -\frac {3}{8}-\frac {{\mathrm e}^{-2 x} \left (x +1\right ) \operatorname {Ei}_{1}\left (-2 x \right )}{4}+\left (c_{1} x +c_{2} \right ) {\mathrm e}^{-2 x}+\frac {\ln \left (x \right ) \left (x -1\right )}{4} \]

✓ Solution by Mathematica

Time used: 0.082 (sec). Leaf size: 52

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

\[ y(x)\to \frac {1}{8} e^{-2 x} \left (2 (x+1) \operatorname {ExpIntegralEi}(2 x)-3 e^{2 x}+2 e^{2 x} (x-1) \log (x)+8 c_2 x+8 c_1\right ) \]