28.2.62 problem 62

Internal problem ID [4505]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 62
Date solved : Monday, January 27, 2025 at 09:21:59 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=15 \,{\mathrm e}^{-x} \sqrt {1+x} \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 21

dsolve(diff(y(x),x$2)+2*diff(y(x),x)+y(x)=15*exp(-x)*sqrt(1+x),y(x), singsol=all)
 

\[ y \left (x \right ) = {\mathrm e}^{-x} \left (4 \left (x +1\right )^{{5}/{2}}+c_{1} x +c_{2} \right ) \]

✓ Solution by Mathematica

Time used: 0.049 (sec). Leaf size: 27

DSolve[D[y[x],{x,2}]+2*D[y[x],x]+y[x]==15*Exp[-x]*Sqrt[1+x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x} \left (4 (x+1)^{5/2}+c_2 x+c_1\right ) \]