80.1.1 problem 2

Internal problem ID [18531]
Book : Elementary Differential Equations. By Thornton C. Fry. D Van Nostrand. NY. First Edition (1929)
Section : Chapter 1. section 5. Problems at page 19
Problem number : 2
Date solved : Tuesday, January 28, 2025 at 08:28:41 PM
CAS classification : [[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]

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

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 20

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

\[ y \left (x \right ) = \frac {\left (c_{2} x +\frac {c_{1}}{2}\right )^{2}}{c_{2} x^{4}} \]

✓ Solution by Mathematica

Time used: 0.245 (sec). Leaf size: 19

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

\[ y(x)\to \frac {c_2 (x+2 c_1){}^2}{x^4} \]