28.2.25 problem 25

Internal problem ID [4468]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 25
Date solved : Monday, January 27, 2025 at 09:19:08 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }-3 y^{\prime }&=9 x^{2} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 39

dsolve(diff(y(x),x$3)-3*diff(y(x),x)=9*x^2,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\sqrt {3}\, {\mathrm e}^{\sqrt {3}\, x} c_{2}}{3}-\frac {\sqrt {3}\, {\mathrm e}^{-\sqrt {3}\, x} c_{1}}{3}-x^{3}-2 x +c_3 \]

✓ Solution by Mathematica

Time used: 0.111 (sec). Leaf size: 52

DSolve[D[y[x],{x,3}]-3*D[y[x],x]==9*x^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -x^3-2 x+\frac {c_1 e^{\sqrt {3} x}}{\sqrt {3}}-\frac {c_2 e^{-\sqrt {3} x}}{\sqrt {3}}+c_3 \]