Internal problem ID [5383]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 15. Linear equations with constant coefficients (Variation of parameters).
Supplemetary problems. Page 98
Problem number: 13.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-y=\sin \left ({\mathrm e}^{-x}\right ) {\mathrm e}^{-x}+\cos \left ({\mathrm e}^{-x}\right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 33
dsolve(diff(y(x),x$2)-y(x)=exp(-x)*sin(exp(-x))+cos(exp(-x)),y(x), singsol=all)
\[ y = c_{2} {\mathrm e}^{-x}+c_{1} {\mathrm e}^{x}-2 \cos \left (\frac {{\mathrm e}^{-x}}{2}\right ) {\mathrm e}^{x} \sin \left (\frac {{\mathrm e}^{-x}}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.166 (sec). Leaf size: 31
DSolve[y''[x]-y[x]==Exp[-x]*Sin[Exp[-x]]+Cos[Exp[-x]],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -e^x \sin \left (e^{-x}\right )+c_1 e^x+c_2 e^{-x} \]