18.2.16 problem Problem 15.34

Internal problem ID [3499]
Book : Mathematical methods for physics and engineering, Riley, Hobson, Bence, second edition, 2002
Section : Chapter 15, Higher order ordinary differential equations. 15.4 Exercises, page 523
Problem number : Problem 15.34
Date solved : Monday, January 27, 2025 at 07:39:49 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} x y^{\prime \prime \prime }+2 y^{\prime \prime }&=A x \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 20

dsolve(x*diff(y(x),x$3)+2*diff(y(x),x$2)=A*x,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {A \,x^{3}}{18}-\ln \left (x \right ) c_{1} +c_{2} x +c_3 \]

✓ Solution by Mathematica

Time used: 0.052 (sec). Leaf size: 26

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

\[ y(x)\to \frac {A x^3}{18}+c_3 x-c_1 \log (x)+c_2 \]