Internal problem ID [557]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.6. Page 100
Problem number: 19.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{3} x^{2}+x \left (1+y^{2}\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 25
dsolve(x^2*y(x)^3+x*(1+y(x)^2)*diff(y(x),x) = 0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{\frac {\LambertW \left ({\mathrm e}^{x^{2}+2 c_{1}}\right )}{2}-\frac {x^{2}}{2}-c_{1}} \]
✓ Solution by Mathematica
Time used: 60.077 (sec). Leaf size: 41
DSolve[x^2*y[x]^3+x*(1+y[x]^2)*y'[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{\sqrt {\text {ProductLog}\left (e^{x^2-2 c_1}\right )}} \\ y(x)\to \frac {1}{\sqrt {\text {ProductLog}\left (e^{x^2-2 c_1}\right )}} \\ \end{align*}