Internal problem ID [6376]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven
Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 2. Problems for Review and Discovery. Drill excercises. Page 105
Problem number: 1(f).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+y={\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 17
dsolve(diff(y(x),x$2)+y(x)=exp(x),y(x), singsol=all)
\[ y \left (x \right ) = \sin \left (x \right ) c_{2} +\cos \left (x \right ) c_{1} +\frac {{\mathrm e}^{x}}{2} \]
✓ Solution by Mathematica
Time used: 0.058 (sec). Leaf size: 23
DSolve[y''[x]+y[x]==Exp[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^x}{2}+c_1 \cos (x)+c_2 \sin (x) \]