15.11.3 problem 3

Internal problem ID [3113]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 19, page 86
Problem number : 3
Date solved : Monday, January 27, 2025 at 07:19:36 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 24

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

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

✓ 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[x],y[x],x,IncludeSingularSolutions -> True]
 

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