Internal problem ID [8288]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 708.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {\left (-y^{2}+4 a x \right )^{3}}{\left (-y^{2}+4 a x -1\right ) y}=0} \end {gather*}
✗ Solution by Maple
dsolve(diff(y(x),x) = (-y(x)^2+4*a*x)^3/(-y(x)^2+4*a*x-1)/y(x),y(x), singsol=all)
\[ \text {No solution found} \]
✓ Solution by Mathematica
Time used: 0.255 (sec). Leaf size: 89
DSolve[y'[x] == (4*a*x - y[x]^2)^3/(y[x]*(-1 + 4*a*x - y[x]^2)),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [2 a \left (x-\frac {\text {RootSum}\left [-\text {$\#$1}^3+2 \text {$\#$1} a-2 a\&,\frac {\text {$\#$1} a \log \left (-\text {$\#$1}+4 a x-y(x)^2\right )-a \log \left (-\text {$\#$1}+4 a x-y(x)^2\right )}{2 a-3 \text {$\#$1}^2}\&\right ]}{2 a}\right )=c_1,y(x)\right ] \]