23.3.24 problem 10

Internal problem ID [4165]
Book : Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section : Chapter 4. The general linear differential equation of order n. Exercises at page 63
Problem number : 10
Date solved : Monday, January 27, 2025 at 08:41:11 AM
CAS classification : [[_3rd_order, _exact, _linear, _homogeneous]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 20

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

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

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 19

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

\[ y(x)\to \frac {x (c_2 x+c_1)}{x+1} \]