Internal problem ID [2007]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 10, page 41
Problem number: 21.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]
\[ \boxed {y+y^{3}+4 \left (x y^{2}-1\right ) y^{\prime }=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.141 (sec). Leaf size: 34
dsolve([(y(x)+y(x)^3)+4*(x*y(x)^2-1)*diff(y(x),x)=0,y(0) = 1],y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{\operatorname {RootOf}\left (-x \,{\mathrm e}^{4 \textit {\_Z}}-2 x \,{\mathrm e}^{2 \textit {\_Z}}+2 \,{\mathrm e}^{2 \textit {\_Z}}+4 \textit {\_Z} -x -2\right )} \]
✓ Solution by Mathematica
Time used: 0.207 (sec). Leaf size: 37
DSolve[{(y[x]+y[x]^3)+4*(x*y[x]^2-1)*y'[x]==0,{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [x=\frac {2 y(x)^2+4 \log (y(x))}{\left (y(x)^2+1\right )^2}-\frac {2}{\left (y(x)^2+1\right )^2},y(x)\right ] \]