74.15.18 problem 18

Internal problem ID [16457]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.7, page 195
Problem number : 18
Date solved : Tuesday, January 28, 2025 at 09:08:22 AM
CAS classification : [[_3rd_order, _exact, _linear, _homogeneous]]

\begin{align*} x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-2 x y^{\prime }-2 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 19

dsolve(x^3*diff(y(x),x$3)+3*x^2*diff(y(x),x$2)-2*x*diff(y(x),x)-2*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 23

DSolve[x^3*D[y[x],{x,3}]+3*x^2*D[y[x],{x,2}]-2*x*D[y[x],x]-2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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