40.10.4 problem 13

Internal problem ID [6726]
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
Date solved : Monday, January 27, 2025 at 02:25:08 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-y&={\mathrm e}^{-x} \sin \left ({\mathrm e}^{-x}\right )+\cos \left ({\mathrm e}^{-x}\right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 24

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

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

✓ Solution by Mathematica

Time used: 0.154 (sec). Leaf size: 31

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

\[ y(x)\to -e^x \sin \left (e^{-x}\right )+c_1 e^x+c_2 e^{-x} \]