53.1.1 problem 1

Internal problem ID [8435]
Book : Elementary differential equations. By Earl D. Rainville, Phillip E. Bedient. Macmilliam Publishing Co. NY. 6th edition. 1981.
Section : CHAPTER 16. Nonlinear equations. Section 94. Factoring the left member. EXERCISES Page 309
Problem number : 1
Date solved : Monday, January 27, 2025 at 04:00:31 PM
CAS classification : [_separable]

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

✓ Solution by Maple

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

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

\begin{align*} y &= c_{1} x \\ y &= \frac {c_{1}}{x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.042 (sec). Leaf size: 24

DSolve[x^2*(D[y[x],x])^2-y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {c_1}{x} \\ y(x)\to c_1 x \\ y(x)\to 0 \\ \end{align*}