Internal problem ID [6389]
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: 3(c).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-y^{\prime }-2 y=\cos \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 25
dsolve(diff(y(x),x$2)-diff(y(x),x)-2*y(x)=cos(x),y(x), singsol=all)
\[ y \left (x \right ) = c_{2} {\mathrm e}^{-x}+{\mathrm e}^{2 x} c_{1} -\frac {3 \cos \left (x \right )}{10}-\frac {\sin \left (x \right )}{10} \]
✓ Solution by Mathematica
Time used: 0.056 (sec). Leaf size: 34
DSolve[y''[x]-y'[x]-2*y[x]==Cos[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {\sin (x)}{10}-\frac {3 \cos (x)}{10}+c_1 e^{-x}+c_2 e^{2 x} \]