Internal problem ID [8296]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 716.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {3 x^{4}+3 x^{3}+\sqrt {9 x^{4}-4 y^{3}}}{\left (x +1\right ) y^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 37
dsolve(diff(y(x),x) = (3*x^4+3*x^3+(9*x^4-4*y(x)^3)^(1/2))/(x+1)/y(x)^2,y(x), singsol=all)
\[ \int _{\textit {\_b}}^{y \relax (x )}\frac {\textit {\_a}^{2}}{\sqrt {9 x^{4}-4 \textit {\_a}^{3}}}d \textit {\_a} -\ln \left (x +1\right )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 3.311 (sec). Leaf size: 133
DSolve[y'[x] == (3*x^3 + 3*x^4 + Sqrt[9*x^4 - 4*y[x]^3])/((1 + x)*y[x]^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \left (-\frac {3}{2}\right )^{2/3} \sqrt [3]{x^4-4 \log ^2(x+1)+8 c_1 \log (x+1)-4 c_1{}^2} \\ y(x)\to \left (\frac {3}{2}\right )^{2/3} \sqrt [3]{x^4-4 \log ^2(x+1)+8 c_1 \log (x+1)-4 c_1{}^2} \\ y(x)\to -\sqrt [3]{-1} \left (\frac {3}{2}\right )^{2/3} \sqrt [3]{x^4-4 \log ^2(x+1)+8 c_1 \log (x+1)-4 c_1{}^2} \\ \end{align*}