40.11.13 problem 39

Internal problem ID [6747]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 16. Linear equations with constant coefficients (Short methods). Supplemetary problems. Page 107
Problem number : 39
Date solved : Monday, January 27, 2025 at 02:27:20 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-y&=x \,{\mathrm e}^{3 x} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 26

dsolve(diff(y(x),x$2)-y(x)=x*exp(3*x),y(x), singsol=all)
 

\[ y = c_2 \,{\mathrm e}^{-x}+{\mathrm e}^{x} c_1 +\frac {\left (4 x -3\right ) {\mathrm e}^{3 x}}{32} \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 34

DSolve[D[y[x],{x,2}]-y[x]==x*Exp[3*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{32} e^{3 x} (4 x-3)+c_1 e^x+c_2 e^{-x} \]