6.23 problem 23

Internal problem ID [4321]

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.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]

Solve \begin {gather*} \boxed {y^{\prime \prime }+y-2 x \,{\mathrm e}^{x}=0} \end {gather*}

Solution by Maple

Time used: 0.005 (sec). Leaf size: 19

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

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

Solution by Mathematica

Time used: 0.05 (sec). Leaf size: 23

DSolve[y''[x]+y[x]==2*x*Exp[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to e^x (x-1)+c_1 \cos (x)+c_2 \sin (x) \\ \end{align*}