Internal problem ID [8425]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 845.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [NONE]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {3 x^{3}+\sqrt {-9 x^{4}+4 y^{3}}+x^{2} \sqrt {-9 x^{4}+4 y^{3}}+x^{3} \sqrt {-9 x^{4}+4 y^{3}}}{y^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 44
dsolve(diff(y(x),x) = (3*x^3+(-9*x^4+4*y(x)^3)^(1/2)+x^2*(-9*x^4+4*y(x)^3)^(1/2)+x^3*(-9*x^4+4*y(x)^3)^(1/2))/y(x)^2,y(x), singsol=all)
\[ \int _{\textit {\_b}}^{y \relax (x )}\frac {\textit {\_a}^{2}}{\sqrt {-9 x^{4}+4 \textit {\_a}^{3}}}d \textit {\_a} -\frac {x^{4}}{4}-\frac {x^{3}}{3}-x -c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 4.212 (sec). Leaf size: 197
DSolve[y'[x] == (3*x^3 + Sqrt[-9*x^4 + 4*y[x]^3] + x^2*Sqrt[-9*x^4 + 4*y[x]^3] + x^3*Sqrt[-9*x^4 + 4*y[x]^3])/y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{2} \sqrt [3]{-\frac {1}{2}} \sqrt [3]{\left (\left (x \left (x (3 x+4)^2+72\right )+132\right ) x^2+144\right ) x^2+24 c_1 \left ((3 x+4) x^2+12\right ) x+144 c_1{}^2} \\ y(x)\to \frac {1}{2} \sqrt [3]{\frac {1}{2} \left (x \left (x (3 x+4)^2+72\right )+132\right ) x^4+72 x^2+12 c_1 \left ((3 x+4) x^2+12\right ) x+72 c_1{}^2} \\ y(x)\to \frac {1}{2} (-1)^{2/3} \sqrt [3]{\frac {1}{2} \left (x \left (x (3 x+4)^2+72\right )+132\right ) x^4+72 x^2+12 c_1 \left ((3 x+4) x^2+12\right ) x+72 c_1{}^2} \\ \end{align*}