Internal problem ID [2017]
Book: Mathematical methods for physics and engineering, Riley, Hobson, Bence, second edition,
2002
Section: Chapter 15, Higher order ordinary differential equations. 15.4 Exercises, page
523
Problem number: Problem 15.24(b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-2 y^{\prime }+y-2 \,{\mathrm e}^{x} x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 21
dsolve(diff(y(x),x$2)-2*diff(y(x),x)+y(x)=2*x*exp(x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} {\mathrm e}^{x}+x \,{\mathrm e}^{x} c_{1}+\frac {{\mathrm e}^{x} x^{3}}{3} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 25
DSolve[y''[x]-2*y'[x]+y[x]==2*x*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{3} e^x \left (x^3+3 c_2 x+3 c_1\right ) \\ \end{align*}