15.7.21 problem 21

Internal problem ID [3002]
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
Date solved : Monday, January 27, 2025 at 07:07:11 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

\begin{align*} 1+x y \left (1+x y^{2}\right ) y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.261 (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: 0.000 (sec). Leaf size: 0

DSolve[{1+x*y[x]*(1+x*y[x]^2)*D[y[x],x]==0,{y[1]==0}},y[x],x,IncludeSingularSolutions -> True]
 

{}