15.19.1 problem 1

Internal problem ID [3285]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 37, page 171
Problem number : 1
Date solved : Monday, January 27, 2025 at 07:30:58 AM
CAS classification : [_separable]

\begin{align*} 4 y^{2}&={y^{\prime }}^{2} x^{2} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 17

dsolve(4*y(x)^2=diff(y(x),x)^2*x^2,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= c_{1} x^{2} \\ y \left (x \right ) &= \frac {c_{1}}{x^{2}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.047 (sec). Leaf size: 26

DSolve[4*y[x]^2==D[y[x],x]^2*x^2,y[x],x,IncludeSingularSolutions -> True]
 

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