Internal problem ID [594]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Miscellaneous problems, end of chapter 2. Page 133
Problem number: 27.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_1st_order, _with_symmetry_[F(x)*G(y),0]]]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {x}{x^{2}+y+y^{3}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 40
dsolve(diff(y(x),x) = x/(x^2+y(x)+y(x)^3),y(x), singsol=all)
\[ c_{1}-{\mathrm e}^{-2 y \relax (x )} x^{2}-\frac {\left (4 y \relax (x )^{3}+6 y \relax (x )^{2}+10 y \relax (x )+5\right ) {\mathrm e}^{-2 y \relax (x )}}{4} = 0 \]
✓ Solution by Mathematica
Time used: 0.176 (sec). Leaf size: 48
DSolve[y'[x] == x/(x^2+y[x]+y[x]^3),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-\frac {1}{2} x^2 e^{-2 y(x)}-\frac {1}{8} e^{-2 y(x)} \left (4 y(x)^3+6 y(x)^2+10 y(x)+5\right )=c_1,y(x)\right ] \]