39.3.4 problem Problem 12.4

Internal problem ID [6530]
Book : Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill 2014
Section : Chapter 12. VARIATION OF PARAMETERS. page 104
Problem number : Problem 12.4
Date solved : Monday, January 27, 2025 at 02:11:36 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&={\mathrm e}^{3 x} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 23

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

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

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 31

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

\[ y(x)\to \frac {e^{3 x}}{4}+c_1 e^{-x}+c_2 e^{2 x} \]