Internal problem ID [8300]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 720.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [y=_G(x,y')]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {x^{3} \left (3 x +3+\sqrt {9 x^{4}-4 y^{3}}\right )}{\left (x +1\right ) y^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 48
dsolve(diff(y(x),x) = x^3*(3*x+3+(9*x^4-4*y(x)^3)^(1/2))/(x+1)/y(x)^2,y(x), singsol=all)
\[ \int _{\textit {\_b}}^{y \relax (x )}\frac {\textit {\_a}^{2}}{\sqrt {9 x^{4}-4 \textit {\_a}^{3}}}d \textit {\_a} -\frac {x^{3}}{3}+\frac {x^{2}}{2}-x +\ln \left (x +1\right )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 3.889 (sec). Leaf size: 321
DSolve[y'[x] == (x^3*(3 + 3*x + Sqrt[9*x^4 - 4*y[x]^3]))/((1 + x)*y[x]^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sqrt [3]{-4 x^6+12 x^5-24 x^4+8 (-1+3 c_1) x^3-6 (-5+6 c_1) x^2+12 \left (2 x^3-3 x^2+6 x+11-6 c_1\right ) \log (x+1)-36 \log ^2(x+1)+12 (-11+6 c_1) x-(11-6 c_1){}^2}}{2^{2/3}} \\ y(x)\to -\frac {\sqrt [3]{-1} \sqrt [3]{-4 x^6+12 x^5-24 x^4+8 (-1+3 c_1) x^3-6 (-5+6 c_1) x^2+12 \left (2 x^3-3 x^2+6 x+11-6 c_1\right ) \log (x+1)-36 \log ^2(x+1)+12 (-11+6 c_1) x-(11-6 c_1){}^2}}{2^{2/3}} \\ y(x)\to \left (-\frac {1}{2}\right )^{2/3} \sqrt [3]{-4 x^6+12 x^5-24 x^4+8 (-1+3 c_1) x^3-6 (-5+6 c_1) x^2+12 \left (2 x^3-3 x^2+6 x+11-6 c_1\right ) \log (x+1)-36 \log ^2(x+1)+12 (-11+6 c_1) x-(11-6 c_1){}^2} \\ \end{align*}