28.2.35 problem 35

Internal problem ID [4478]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 35
Date solved : Monday, January 27, 2025 at 09:20:36 AM
CAS classification : [[_high_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 22

dsolve(diff(y(x),x$4)-diff(y(x),x$2)=2*exp(x),y(x), singsol=all)
 

\[ y \left (x \right ) = {\mathrm e}^{-x} c_{1} +\left (x +c_{2} -2\right ) {\mathrm e}^{x}+x c_3 +c_4 \]

✓ Solution by Mathematica

Time used: 0.135 (sec). Leaf size: 31

DSolve[D[y[x],{x,4}]-D[y[x],{x,2}]==2*Exp[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x \left (x-\frac {5}{2}+c_1\right )+c_2 e^{-x}+c_4 x+c_3 \]