Internal problem ID [8252]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 672.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [y=_G(x,y')]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {x^{2} \left (3 x +\sqrt {-9 x^{4}+4 y^{3}}\right )}{y^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 36
dsolve(diff(y(x),x) = x^2*(3*x+(-9*x^4+4*y(x)^3)^(1/2))/y(x)^2,y(x), singsol=all)
\[ \int _{\textit {\_b}}^{y \relax (x )}\frac {\textit {\_a}^{2}}{\sqrt {-9 x^{4}+4 \textit {\_a}^{3}}}d \textit {\_a} -\frac {x^{3}}{3}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 21.151 (sec). Leaf size: 4512
DSolve[y'[x] == (x^2*(3*x + Sqrt[-9*x^4 + 4*y[x]^3]))/y[x]^2,y[x],x,IncludeSingularSolutions -> True]
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