Internal problem ID [8460]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 880.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime }+\frac {2 a}{-y-2 a -2 y^{4} a +16 y^{2} a^{2} x -32 a^{3} x^{2}-2 y^{6} a +24 y^{4} a^{2} x -96 y^{2} a^{3} x^{2}+128 a^{4} x^{3}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.084 (sec). Leaf size: 41
dsolve(diff(y(x),x) = -2*a/(-y(x)-2*a-2*a*y(x)^4+16*a^2*x*y(x)^2-32*a^3*x^2-2*a*y(x)^6+24*y(x)^4*a^2*x-96*y(x)^2*a^3*x^2+128*a^4*x^3),y(x), singsol=all)
\[ \frac {y \relax (x )}{2 a}+\frac {\int _{}^{-4 a x +y \relax (x )^{2}}\frac {1}{\textit {\_a}^{3}+\textit {\_a}^{2}+1}d \textit {\_a}}{8 a^{2}}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.331 (sec). Leaf size: 131
DSolve[y'[x] == (-2*a)/(-2*a - 32*a^3*x^2 + 128*a^4*x^3 - y[x] + 16*a^2*x*y[x]^2 - 96*a^3*x^2*y[x]^2 - 2*a*y[x]^4 + 24*a^2*x*y[x]^4 - 2*a*y[x]^6),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {\text {RootSum}\left [-64 \text {$\#$1}^3 a^3+48 \text {$\#$1}^2 a^2 y(x)^2+16 \text {$\#$1}^2 a^2-12 \text {$\#$1} a y(x)^4-8 \text {$\#$1} a y(x)^2+y(x)^6+y(x)^4+1\&,\frac {\log (x-\text {$\#$1})}{48 \text {$\#$1}^2 a^2-24 \text {$\#$1} a y(x)^2-8 \text {$\#$1} a+3 y(x)^4+2 y(x)^2}\&\right ]}{8 a^2}+\frac {y(x)}{2 a}=c_1,y(x)\right ] \]