Internal problem ID [8599]
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]
\[ \boxed {y^{\prime } y+3 x^{2} y^{2}=-2 x^{3}-7} \]
✓ Solution by Maple
Time used: 0.063 (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 \left (x \right ) = -\frac {2^{\frac {2}{3}} \sqrt {3}\, \sqrt {\left (-x^{3}\right )^{\frac {1}{3}} \Gamma \left (\frac {2}{3}\right ) 2^{\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}}-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 )-80 \,{\mathrm e}^{-2 x^{3}} x \pi \sqrt {3}\right )}}{18 \left (-x^{3}\right )^{\frac {1}{3}} \Gamma \left (\frac {2}{3}\right )} y \left (x \right ) = \frac {2^{\frac {2}{3}} \sqrt {3}\, \sqrt {\left (-x^{3}\right )^{\frac {1}{3}} \Gamma \left (\frac {2}{3}\right ) 2^{\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}}-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 )-80 \,{\mathrm e}^{-2 x^{3}} x \pi \sqrt {3}\right )}}{18 \left (-x^{3}\right )^{\frac {1}{3}} \Gamma \left (\frac {2}{3}\right )} \end{align*}
✓ Solution by Mathematica
Time used: 4.884 (sec). Leaf size: 166
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 {\sqrt {\frac {e^{-2 x^3} \left (-7\ 2^{2/3} \left (-x^3\right )^{2/3} \Gamma \left (\frac {1}{3},-2 x^3\right )+2^{2/3} \left (-x^3\right )^{2/3} \Gamma \left (\frac {4}{3},-2 x^3\right )+3 c_1 x^2\right )}{x^2}}}{\sqrt {3}} y(x)\to \frac {\sqrt {\frac {e^{-2 x^3} \left (-7\ 2^{2/3} \left (-x^3\right )^{2/3} \Gamma \left (\frac {1}{3},-2 x^3\right )+2^{2/3} \left (-x^3\right )^{2/3} \Gamma \left (\frac {4}{3},-2 x^3\right )+3 c_1 x^2\right )}{x^2}}}{\sqrt {3}} \end{align*}