35.6.23 problem 23

Internal problem ID [6173]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 6. SECOND-ORDER LINEAR EQUATIONSWITH CONSTANT COEFFICIENTS AND RIGHT-HAND SIDE NOT ZERO. page 422
Problem number : 23
Date solved : Monday, January 27, 2025 at 01:46:30 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+y&=2 x \,{\mathrm e}^{x} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 19

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

\[ y = \sin \left (x \right ) c_2 +\cos \left (x \right ) c_1 +\left (x -1\right ) {\mathrm e}^{x} \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 23

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

\[ y(x)\to e^x (x-1)+c_1 \cos (x)+c_2 \sin (x) \]