35.6.7 problem 7

Internal problem ID [6157]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 6. SECOND-ORDER LINEAR EQUATIONSWITH CONSTANT COEFFICIENTS AND RIGHT-HAND SIDE NOT ZERO. page 422
Problem number : 7
Date solved : Monday, January 27, 2025 at 01:38:40 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 19

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

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

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 27

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

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