Internal problem ID [10114]
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 9. Variables
searated or separable. Page 13
Problem number: Ex 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left (x +1\right ) y^{2}-x^{3} y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 22
dsolve((1+x)*y(x)^2-x^3*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {2 x^{2}}{2 x^{2} c_{1}+2 x +1} \]
✓ Solution by Mathematica
Time used: 0.145 (sec). Leaf size: 29
DSolve[(1+x)*y[x]^2-x^3*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2 x^2}{-2 c_1 x^2+2 x+1} \\ y(x)\to 0 \\ \end{align*}