50.14.20 problem 3(d)

Internal problem ID [8058]
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(d)
Date solved : Monday, January 27, 2025 at 03:40:31 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 44

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

\[ y = {\mathrm e}^{-\left (1+\sqrt {2}\right ) x} c_{1} +{\mathrm e}^{\left (\sqrt {2}-1\right ) x} c_{2} -\frac {4 \left (\left (x -\frac {31}{34}\right ) \cos \left (x \right )-\frac {\sin \left (x \right ) \left (x +\frac {44}{17}\right )}{4}\right ) {\mathrm e}^{x}}{17} \]

✓ Solution by Mathematica

Time used: 0.034 (sec). Leaf size: 59

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

\[ y(x)\to c_1 e^{-\left (\left (1+\sqrt {2}\right ) x\right )}+c_2 e^{\left (\sqrt {2}-1\right ) x}+\frac {1}{289} e^x ((17 x+44) \sin (x)+(62-68 x) \cos (x)) \]