73.17.19 problem 19

Internal problem ID [15553]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 25. Review exercises for part III. page 447
Problem number : 19
Date solved : Tuesday, January 28, 2025 at 08:01:55 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{2} y^{\prime \prime }+2 x y^{\prime }-30 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 15

dsolve(x^2*diff(y(x),x$2)+2*x*diff(y(x),x)-30*y(x)=0,y(x), singsol=all)
 

\[ y = c_{1} x^{5}+\frac {c_{2}}{x^{6}} \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 18

DSolve[x^2*D[y[x],{x,2}]+2*x*D[y[x],x]-30*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_1}{x^6}+c_2 x^5 \]