28.2.61 problem 61

Internal problem ID [4504]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 61
Date solved : Monday, January 27, 2025 at 09:21:56 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-y&={\mathrm e}^{-2 x} \sin \left ({\mathrm e}^{-x}\right ) \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 33

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

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

✓ Solution by Mathematica

Time used: 0.099 (sec). Leaf size: 39

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

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