Internal problem ID [10120]
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]
Solve \begin {gather*} \boxed {2 x^{2} y+y^{3}-x^{3} y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (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 \relax (x ) = \frac {x^{2}}{\sqrt {-x^{2}+c_{1}}} \\ y \relax (x ) = -\frac {x^{2}}{\sqrt {-x^{2}+c_{1}}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.191 (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*}