64.13.3 problem 3

Internal problem ID [13533]
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 : 3
Date solved : Tuesday, January 28, 2025 at 05:52:06 AM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 13

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

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

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 18

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

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