Internal problem ID [7843]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 263.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Bernoulli]
Solve \begin {gather*} \boxed {2 x^{3}+y y^{\prime }+3 y^{2} x^{2}+7=0} \end {gather*}
✓ Solution by Maple
Time used: 0.172 (sec). Leaf size: 211
dsolve(2*x^3+y(x)*diff(y(x),x)+3*x^2*y(x)^2+7=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {2^{\frac {2}{3}} \sqrt {3}\, \sqrt {\Gamma \left (\frac {2}{3}\right ) 2^{\frac {1}{3}} \left (-x^{3}\right )^{\frac {1}{3}} \left (27 \,{\mathrm e}^{-2 x^{3}} c_{1} \Gamma \left (\frac {2}{3}\right ) 2^{\frac {1}{3}} \left (-x^{3}\right )^{\frac {1}{3}}+120 \,{\mathrm e}^{-2 x^{3}} x \Gamma \left (\frac {1}{3}, -2 x^{3}\right ) \Gamma \left (\frac {2}{3}\right )-80 \,{\mathrm e}^{-2 x^{3}} x \pi \sqrt {3}-18 x \Gamma \left (\frac {2}{3}\right ) 2^{\frac {1}{3}} \left (-x^{3}\right )^{\frac {1}{3}}\right )}}{18 \Gamma \left (\frac {2}{3}\right ) \left (-x^{3}\right )^{\frac {1}{3}}} \\ y \relax (x ) = \frac {2^{\frac {2}{3}} \sqrt {3}\, \sqrt {\Gamma \left (\frac {2}{3}\right ) 2^{\frac {1}{3}} \left (-x^{3}\right )^{\frac {1}{3}} \left (27 \,{\mathrm e}^{-2 x^{3}} c_{1} \Gamma \left (\frac {2}{3}\right ) 2^{\frac {1}{3}} \left (-x^{3}\right )^{\frac {1}{3}}+120 \,{\mathrm e}^{-2 x^{3}} x \Gamma \left (\frac {1}{3}, -2 x^{3}\right ) \Gamma \left (\frac {2}{3}\right )-80 \,{\mathrm e}^{-2 x^{3}} x \pi \sqrt {3}-18 x \Gamma \left (\frac {2}{3}\right ) 2^{\frac {1}{3}} \left (-x^{3}\right )^{\frac {1}{3}}\right )}}{18 \Gamma \left (\frac {2}{3}\right ) \left (-x^{3}\right )^{\frac {1}{3}}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 4.821 (sec). Leaf size: 83
DSolve[2*x^3+y[x]*y'[x]+3*x^2*y[x]^2+7==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{3} \sqrt {-6 x+e^{-2 x^3} \left (40 x E_{\frac {2}{3}}\left (-2 x^3\right )+9 c_1\right )} \\ y(x)\to \frac {1}{3} \sqrt {-6 x+e^{-2 x^3} \left (40 x E_{\frac {2}{3}}\left (-2 x^3\right )+9 c_1\right )} \\ \end{align*}