7.11.54 problem 56

Internal problem ID [375]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.5 (Nonhomogeneous equations and undetermined coefficients). Problems at page 161
Problem number : 56
Date solved : Monday, January 27, 2025 at 02:47:43 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-4 y&=x \,{\mathrm e}^{x} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 34

dsolve(diff(y(x),x$2)-4*y(x)=x*exp(x),y(x), singsol=all)
 

\[ y = -\frac {\left (-9 \,{\mathrm e}^{4 x} c_1 +3 x \,{\mathrm e}^{3 x}+2 \,{\mathrm e}^{3 x}-9 c_2 \right ) {\mathrm e}^{-2 x}}{9} \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 34

DSolve[D[y[x],{x,2}]-4*y[x]==x*Exp[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {1}{9} e^x (3 x+2)+c_1 e^{2 x}+c_2 e^{-2 x} \]