Internal problem ID [3096]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 12
Problem number: 348.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime } x^{3}-\left (x +1\right ) y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 22
dsolve(x^3*diff(y(x),x) = (1+x)*y(x)^2,y(x), singsol=all)
\[ y \relax (x ) = \frac {2 x^{2}}{2 c_{1} x^{2}+2 x +1} \]
✓ Solution by Mathematica
Time used: 0.14 (sec). Leaf size: 29
DSolve[x^3 y'[x]==(1+x)y[x]^2,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*}