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^{\prime } y+3 x^{2} y^{2}+7=0} \end {gather*}
✓ Solution by Maple
Time used: 0.082 (sec). Leaf size: 207
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 \,2^{\frac {1}{3}} \left (-x^{3}\right )^{\frac {1}{3}} \Gamma \left (\frac {2}{3}\right ) \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}}+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}}-120 \,{\mathrm e}^{-2 x^{3}} x \Gamma \left (\frac {1}{3}, -2 x^{3}\right ) \Gamma \left (\frac {2}{3}\right )\right )}}{18 \left (-x^{3}\right )^{\frac {1}{3}} \Gamma \left (\frac {2}{3}\right )} \\ y \relax (x ) = \frac {2^{\frac {2}{3}} \sqrt {-3 \,2^{\frac {1}{3}} \left (-x^{3}\right )^{\frac {1}{3}} \Gamma \left (\frac {2}{3}\right ) \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}}+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}}-120 \,{\mathrm e}^{-2 x^{3}} x \Gamma \left (\frac {1}{3}, -2 x^{3}\right ) \Gamma \left (\frac {2}{3}\right )\right )}}{18 \left (-x^{3}\right )^{\frac {1}{3}} \Gamma \left (\frac {2}{3}\right )} \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.764 (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 \operatorname {ExpIntegralE}\left (\frac {2}{3},-2 x^3\right )+9 c_1\right )} \\ y(x)\to \frac {1}{3} \sqrt {-6 x+e^{-2 x^3} \left (40 x \operatorname {ExpIntegralE}\left (\frac {2}{3},-2 x^3\right )+9 c_1\right )} \\ \end{align*}