50.10.10 problem 1(j)

Internal problem ID [7979]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 2. Second-Order Linear Equations. Section 2.2. THE METHOD OF UNDETERMINED COEFFICIENTS. Page 67
Problem number : 1(j)
Date solved : Monday, January 27, 2025 at 03:35:02 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 25

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

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

✓ Solution by Mathematica

Time used: 0.037 (sec). Leaf size: 28

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

\[ y(x)\to -\frac {1}{2} e^x ((x-2 c_2) \cos (x)-2 c_1 \sin (x)) \]