77.1.104 problem Example 2 (page 195)

Internal problem ID [17994]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : Example 2 (page 195)
Date solved : Tuesday, January 28, 2025 at 11:19:34 AM
CAS classification : [[_3rd_order, _fully, _exact, _linear]]

\begin{align*} y^{\prime \prime \prime }-\frac {3 y^{\prime \prime }}{x}+\frac {6 y^{\prime }}{x^{2}}-\frac {6 y}{x^{3}}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 16

dsolve(diff(y(x),x$3)-3/x*diff(y(x),x$2)+6/x^2*diff(y(x),x)-6/x^3*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

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

DSolve[D[y[x],{x,3}]-3/x*D[y[x],{x,2}]+6/x^2*D[y[x],x]-6/x^3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x (x (c_3 x+c_2)+c_1) \]