Internal problem ID [11144]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter 2, differential equations of the first order and the first degree. Article 10.
Homogeneous equations. Page 15
Problem number: Ex 4.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _Bernoulli]
\[ \boxed {2 y x^{2}+y^{3}-x^{3} y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 34
dsolve(2*x^2*y(x)+y(x)^3-x^3*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {x^{2}}{\sqrt {-x^{2}+c_{1}}} y \left (x \right ) = -\frac {x^{2}}{\sqrt {-x^{2}+c_{1}}} \end{align*}
✓ Solution by Mathematica
Time used: 0.181 (sec). Leaf size: 47
DSolve[2*x^2*y[x]+y[x]^3-x^3*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x^2}{\sqrt {-x^2+c_1}} y(x)\to \frac {x^2}{\sqrt {-x^2+c_1}} y(x)\to 0 \end{align*}