78.14.4 problem 3 (b)

Internal problem ID [18340]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 3. Second order linear equations. Section 19. The Method of Variation of Parameters. Problems at page 135
Problem number : 3 (b)
Date solved : Tuesday, January 28, 2025 at 11:47:30 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&={\mathrm e}^{-x} \ln \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 30

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

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

✓ Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 36

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

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