Internal problem ID [2314]
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.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_separable]
\[ \boxed {4 y^{2}-{y^{\prime }}^{2} x^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (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: 0.038 (sec). Leaf size: 26
DSolve[4*y[x]^2==y'[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*}