Internal problem ID [8458]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 878.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {1+y^{4}-8 y^{2} a x +16 a^{2} x^{2}+y^{6}-12 y^{4} a x +48 y^{2} a^{2} x^{2}-64 a^{3} x^{3}}{y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.017 (sec). Leaf size: 75
dsolve(diff(y(x),x) = (1+y(x)^4-8*a*x*y(x)^2+16*a^2*x^2+y(x)^6-12*y(x)^4*a*x+48*y(x)^2*a^2*x^2-64*a^3*x^3)/y(x),y(x), singsol=all)
\[ \int _{\textit {\_b}}^{y \relax (x )}\frac {\textit {\_a}}{-\textit {\_a}^{6}+12 \textit {\_a}^{4} a x -48 \textit {\_a}^{2} a^{2} x^{2}+64 x^{3} a^{3}-\textit {\_a}^{4}+8 \textit {\_a}^{2} a x -16 a^{2} x^{2}+2 a -1}d \textit {\_a} +x -c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.283 (sec). Leaf size: 130
DSolve[y'[x] == (1 + 16*a^2*x^2 - 64*a^3*x^3 - 8*a*x*y[x]^2 + 48*a^2*x^2*y[x]^2 + y[x]^4 - 12*a*x*y[x]^4 + y[x]^6)/y[x],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [2 a \left (x-\frac {1}{2} \text {RootSum}\left [64 \text {$\#$1}^3 a^3-48 \text {$\#$1}^2 a^2 y(x)^2-16 \text {$\#$1}^2 a^2+12 \text {$\#$1} a y(x)^4+8 \text {$\#$1} a y(x)^2+2 a-y(x)^6-y(x)^4-1\&,\frac {\log (x-\text {$\#$1})}{48 \text {$\#$1}^2 a^2-24 \text {$\#$1} a y(x)^2-8 \text {$\#$1} a+3 y(x)^4+2 y(x)^2}\&\right ]\right )=c_1,y(x)\right ] \]