35.6.3 problem 3

Internal problem ID [6153]
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 : 3
Date solved : Monday, January 27, 2025 at 01:38:33 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 25

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

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

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 29

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

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