Internal problem ID [7621]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 40.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Abel]
Solve \begin {gather*} \boxed {y^{\prime }+3 a y^{3}+6 a x y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 48
dsolve(diff(y(x),x) + 3*a*y(x)^3 + 6*a*x*y(x)^2=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {1}{3 a \,x^{2}+\RootOf \left (\left (-3 a \right )^{\frac {1}{3}} \AiryBi \left (\textit {\_Z} \right ) c_{1} x +\left (-3 a \right )^{\frac {1}{3}} x \AiryAi \left (\textit {\_Z} \right )+\AiryBi \left (1, \textit {\_Z}\right ) c_{1}+\AiryAi \left (1, \textit {\_Z}\right )\right ) \left (-3 a \right )^{\frac {1}{3}}} \]
✓ Solution by Mathematica
Time used: 0.526 (sec). Leaf size: 185
DSolve[y'[x] + 3*a*y[x]^3 + 6*a*x*y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {\sqrt [3]{-3} \sqrt [3]{a} x \text {Ai}\left ((-3)^{2/3} a^{2/3} x^2-\frac {(-1)^{2/3}}{\sqrt [3]{3} \sqrt [3]{a} y(x)}\right )+\text {Ai}'\left ((-3)^{2/3} a^{2/3} x^2-\frac {(-1)^{2/3}}{\sqrt [3]{3} \sqrt [3]{a} y(x)}\right )}{\sqrt [3]{-3} \sqrt [3]{a} x \text {Bi}\left ((-3)^{2/3} a^{2/3} x^2-\frac {(-1)^{2/3}}{\sqrt [3]{3} \sqrt [3]{a} y(x)}\right )+\text {Bi}'\left ((-3)^{2/3} a^{2/3} x^2-\frac {(-1)^{2/3}}{\sqrt [3]{3} \sqrt [3]{a} y(x)}\right )}+c_1=0,y(x)\right ] \]