64.13.7 problem 7

Internal problem ID [13537]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.5. The Cauchy-Euler Equation. Exercises page 169
Problem number : 7
Date solved : Tuesday, January 28, 2025 at 05:52:13 AM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} 3 x^{2} y^{\prime \prime }-4 x y^{\prime }+2 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 15

dsolve(3*x^2*diff(y(x),x$2)-4*x*diff(y(x),x)+2*y(x)=0,y(x), singsol=all)
 

\[ y = c_{1} x^{2}+c_{2} x^{{1}/{3}} \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 20

DSolve[3*x^2*D[y[x],{x,2}]-4*x*D[y[x],x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_2 x^2+c_1 \sqrt [3]{x} \]