Internal problem ID [2031]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 11, page 45
Problem number: 21.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]
\[ \boxed {x y \left (1+y^{2} x \right ) y^{\prime }=-1} \] With initial conditions \begin {align*} [y \left (1\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.219 (sec). Leaf size: 66
dsolve([1+x*y(x)*(1+x*y(x)^2)*diff(y(x),x)=0,y(1) = 0],y(x), singsol=all)
\begin{align*} y = \frac {\sqrt {-2 \left (\operatorname {LambertW}\left (-1, -\frac {3 \,{\mathrm e}^{-\frac {2 x +1}{2 x}}}{2}\right ) x +x +\frac {1}{2}\right ) x}}{x} y = -\frac {\sqrt {-2 \left (\operatorname {LambertW}\left (-1, -\frac {3 \,{\mathrm e}^{-\frac {2 x +1}{2 x}}}{2}\right ) x +x +\frac {1}{2}\right ) x}}{x} \end{align*}
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[{1+x*y[x]*(1+x*y[x]^2)*y'[x]==0,{y[1]==0}},y[x],x,IncludeSingularSolutions -> True]
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