53.1.8 problem 8

Internal problem ID [8442]
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 : 8
Date solved : Monday, January 27, 2025 at 04:00:54 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 23

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

\begin{align*} y &= {\mathrm e}^{-\frac {x^{2}}{2}} c_{1} \\ y &= {\mathrm e}^{\frac {x^{2}}{2}} c_{1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.046 (sec). Leaf size: 38

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

\begin{align*} y(x)\to c_1 e^{-\frac {x^2}{2}} \\ y(x)\to c_1 e^{\frac {x^2}{2}} \\ y(x)\to 0 \\ \end{align*}