73.8.17 problem 13.3 (b)

Internal problem ID [15225]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 13. Higher order equations: Extending first order concepts. Additional exercises page 259
Problem number : 13.3 (b)
Date solved : Tuesday, January 28, 2025 at 07:50:23 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} x y^{\prime \prime \prime }+2 y^{\prime \prime }&=6 x \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 19

dsolve(x*diff(y(x),x$3)+2*diff(y(x),x$2)=6*x,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.043 (sec). Leaf size: 25

DSolve[x*D[y[x],{x,3}]+2*D[y[x],{x,2}]==6*x,y[x],x,IncludeSingularSolutions -> True]
 

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