39.2.5 problem Problem 11.48

Internal problem ID [6522]
Book : Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill 2014
Section : Chapter 11. THE METHOD OF UNDETERMINED COEFFICIENTS. Supplementary Problems. page 101
Problem number : Problem 11.48
Date solved : Monday, January 27, 2025 at 02:11:25 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 17

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

\[ y = {\mathrm e}^{x} \left (c_2 +c_1 x +\frac {1}{6} x^{3}\right ) \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 25

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

\[ y(x)\to \frac {1}{6} e^x \left (x^3+6 c_2 x+6 c_1\right ) \]