49.13.7 problem 2

Internal problem ID [7683]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 3. Linear equations with variable coefficients. Page 121
Problem number : 2
Date solved : Monday, January 27, 2025 at 03:09:47 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 16

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

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

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 19

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

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