8.7.28 problem 53

Internal problem ID [834]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.1, second order linear equations. Page 299
Problem number : 53
Date solved : Monday, January 27, 2025 at 03:09:28 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{2} y^{\prime \prime }+2 x y^{\prime }-12 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 15

dsolve(x^2*diff(y(x),x$2)+2*x*diff(y(x),x)-12*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {c_1 \,x^{7}+c_2}{x^{4}} \]

✓ Solution by Mathematica

Time used: 0.010 (sec). Leaf size: 18

DSolve[x^2*D[y[x],{x,2}]+2*x*D[y[x],x]-12*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_2 x^7+c_1}{x^4} \]