28.2.27 problem 27

Internal problem ID [4470]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 27
Date solved : Monday, January 27, 2025 at 09:19:09 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=36 x \,{\mathrm e}^{2 x} \end{align*}

✓ Solution by Maple

Time used: 0.012 (sec). Leaf size: 26

dsolve(diff(y(x),x$2)-diff(y(x),x)-2*y(x)=36*x*exp(2*x),y(x), singsol=all)
 

\[ y \left (x \right ) = \left (6 x^{2}+c_{1} -4 x \right ) {\mathrm e}^{2 x}+c_{2} {\mathrm e}^{-x} \]

✓ Solution by Mathematica

Time used: 0.031 (sec). Leaf size: 34

DSolve[D[y[x],{x,2}]-D[y[x],x]-2*y[x]==36*x*Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{2 x} \left (6 x^2-4 x+\frac {4}{3}+c_2\right )+c_1 e^{-x} \]