28.2.24 problem 24

Internal problem ID [4467]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 24
Date solved : Monday, January 27, 2025 at 09:19:08 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=48 x \,{\mathrm e}^{x} \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 22

dsolve(diff(y(x),x$3)-3*diff(y(x),x$2)+3*diff(y(x),x)-y(x)=48*x*exp(x),y(x), singsol=all)
 

\[ y \left (x \right ) = {\mathrm e}^{x} \left (2 x^{4}+c_3 \,x^{2}+c_{2} x +c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.010 (sec). Leaf size: 27

DSolve[D[y[x],{x,3}]-3*D[y[x],{x,2}]+3*D[y[x],x]-y[x]==48*x*Exp[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x \left (2 x^4+c_3 x^2+c_2 x+c_1\right ) \]