28.2.64 problem 64

Internal problem ID [4507]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 64
Date solved : Monday, January 27, 2025 at 09:22:06 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+y&=\frac {{\mathrm e}^{2 x}}{\left ({\mathrm e}^{x}+1\right )^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 19

dsolve(diff(y(x),x$2)-2*diff(y(x),x)+y(x)=exp(2*x)/(exp(x)+1)^2,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.325 (sec). Leaf size: 24

DSolve[D[y[x],{x,2}]-2*D[y[x],x]+y[x]==Exp[2*x]/(Exp[x]+1)^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x \left (\log \left (e^x+1\right )+(-1+c_2) x+c_1\right ) \]