Internal problem ID [10121]
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 5.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{3}+x^{3} y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 30
dsolve(y(x)^3+x^3*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {x}{\sqrt {x^{2} c_{1}-1}} \\ y \relax (x ) = -\frac {x}{\sqrt {x^{2} c_{1}-1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.36 (sec). Leaf size: 45
DSolve[y[x]^3+x^3*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x}{\sqrt {-1-2 c_1 x^2}} \\ y(x)\to \frac {x}{\sqrt {-1-2 c_1 x^2}} \\ y(x)\to 0 \\ \end{align*}