Internal problem ID [8492]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 912.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {2 a x}{-y x^{3}+2 x^{3} a +2 a y^{4} x^{3}-16 y^{2} a^{2} x^{2}+32 x \,a^{3}+2 a y^{6} x^{3}-24 y^{4} a^{2} x^{2}+96 y^{2} x \,a^{3}-128 a^{4}}=0} \end {gather*}
✗ Solution by Maple
dsolve(diff(y(x),x) = 2*a*x/(-x^3*y(x)+2*x^3*a+2*a*y(x)^4*x^3-16*y(x)^2*a^2*x^2+32*a^3*x+2*a*y(x)^6*x^3-24*y(x)^4*a^2*x^2+96*y(x)^2*x*a^3-128*a^4),y(x), singsol=all)
\[ \text {No solution found} \]
✓ Solution by Mathematica
Time used: 0.653 (sec). Leaf size: 201
DSolve[y'[x] == (2*a*x)/(-128*a^4 + 32*a^3*x + 2*a*x^3 - x^3*y[x] + 96*a^3*x*y[x]^2 - 16*a^2*x^2*y[x]^2 - 24*a^2*x^2*y[x]^4 + 2*a*x^3*y[x]^4 + 2*a*x^3*y[x]^6),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-\text {RootSum}\left [-\text {$\#$1}^3 y(x)^6-\text {$\#$1}^3 y(x)^4-\text {$\#$1}^3+12 \text {$\#$1}^2 a y(x)^4+8 \text {$\#$1}^2 a y(x)^2-48 \text {$\#$1} a^2 y(x)^2-16 \text {$\#$1} a^2+64 a^3\&,\frac {\text {$\#$1} \log (x-\text {$\#$1})}{3 \text {$\#$1}^2 y(x)^6+3 \text {$\#$1}^2 y(x)^4+3 \text {$\#$1}^2-24 \text {$\#$1} a y(x)^4-16 \text {$\#$1} a y(x)^2+48 a^2 y(x)^2+16 a^2}\&\right ]-\frac {\text {RootSum}\left [\text {$\#$1}^3+\text {$\#$1}^2+1\&,\frac {\log \left (y(x)^2-\text {$\#$1}\right )}{3 \text {$\#$1}^2+2 \text {$\#$1}}\&\right ]}{4 a}+y(x)=c_1,y(x)\right ] \]