Internal problem ID [5323]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 9. Equations of first order and higher degree. Supplemetary problems. Page
65
Problem number: 17.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_separable]
\[ \boxed {x^{2} {y^{\prime }}^{2}+x y y^{\prime }-6 y^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(x^2*diff(y(x),x)^2+x*y(x)*diff(y(x),x)-6*y(x)^2=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= c_{1} x^{2} \\ y \left (x \right ) &= \frac {c_{1}}{x^{3}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.044 (sec). Leaf size: 26
DSolve[x^2*(y'[x])^2+x*y[x]*y'[x]-6*y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_1}{x^3} \\ y(x)\to c_1 x^2 \\ y(x)\to 0 \\ \end{align*}