15.16.1 problem 1

Internal problem ID [3221]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 25, page 112
Problem number : 1
Date solved : Monday, January 27, 2025 at 07:26:34 AM
CAS classification : [[_Emden, _Fowler]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 27

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

\[ y = x^{{5}/{2}} \left (x^{\frac {\sqrt {21}}{2}} c_{1} +x^{-\frac {\sqrt {21}}{2}} c_2 \right ) \]

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 34

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

\[ y(x)\to x^{\frac {5}{2}-\frac {\sqrt {21}}{2}} \left (c_2 x^{\sqrt {21}}+c_1\right ) \]