4.2.30 \(3 a (y(x)+2 x) y(x)^2+y'(x)=0\)

ODE
\[ 3 a (y(x)+2 x) y(x)^2+y'(x)=0 \] ODE Classification

[_Abel]

Book solution method
Abel ODE, First kind

Mathematica
cpu = 0.375106 (sec), leaf count = 161

\[\text {Solve}\left [\frac {\sqrt [3]{-3} \sqrt [3]{a} x \text {Ai}\left (\frac {(-1)^{2/3} \left (3 a x^2 y(x)-1\right )}{\sqrt [3]{3} \sqrt [3]{a} y(x)}\right )+\text {Ai}'\left (\frac {(-1)^{2/3} \left (3 a x^2 y(x)-1\right )}{\sqrt [3]{3} \sqrt [3]{a} y(x)}\right )}{\sqrt [3]{-3} \sqrt [3]{a} x \text {Bi}\left (\frac {(-1)^{2/3} \left (3 a x^2 y(x)-1\right )}{\sqrt [3]{3} \sqrt [3]{a} y(x)}\right )+\text {Bi}'\left (\frac {(-1)^{2/3} \left (3 a x^2 y(x)-1\right )}{\sqrt [3]{3} \sqrt [3]{a} y(x)}\right )}+c_1=0,y(x)\right ]\]

Maple
cpu = 0.036 (sec), leaf count = 110

\[ \left \{ {\it \_C1}+{1 \left (\sqrt [3]{-3\,a}x{{\rm Ai}\left (\left (-3\,a \right ) ^{{\frac {2}{3}}}{x}^{2}+{\frac {1}{y \relax (x ) }{\frac {1}{\sqrt [3]{-3\,a}}}}\right )}+{{\rm Ai}^{(1)}\left (\left (-3\,a \right ) ^{{\frac {2}{3}}}{x}^{2}+{\frac {1}{y \relax (x ) }{\frac {1}{\sqrt [3]{-3\,a}}}}\right )} \right ) \left (\sqrt [3]{-3\,a}x{{\rm Bi}\left (\left (-3\,a \right ) ^{{\frac {2}{3}}}{x}^{2}+{\frac {1}{y \relax (x ) }{\frac {1}{\sqrt [3]{-3\,a}}}}\right )}+{{\rm Bi}^{(1)}\left (\left (-3\,a \right ) ^{{\frac {2}{3}}}{x}^{2}+{\frac {1}{y \relax (x ) }{\frac {1}{\sqrt [3]{-3\,a}}}}\right )} \right ) ^{-1}}=0 \right \} \] Mathematica raw input

DSolve[3*a*y[x]^2*(2*x + y[x]) + y'[x] == 0,y[x],x]

Mathematica raw output

Solve[((-3)^(1/3)*a^(1/3)*x*AiryAi[((-1)^(2/3)*(-1 + 3*a*x^2*y[x]))/(3^(1/3)*a^(
1/3)*y[x])] + AiryAiPrime[((-1)^(2/3)*(-1 + 3*a*x^2*y[x]))/(3^(1/3)*a^(1/3)*y[x]
)])/((-3)^(1/3)*a^(1/3)*x*AiryBi[((-1)^(2/3)*(-1 + 3*a*x^2*y[x]))/(3^(1/3)*a^(1/
3)*y[x])] + AiryBiPrime[((-1)^(2/3)*(-1 + 3*a*x^2*y[x]))/(3^(1/3)*a^(1/3)*y[x])]
) + C[1] == 0, y[x]]

Maple raw input

dsolve(diff(y(x),x)+3*a*(2*x+y(x))*y(x)^2 = 0, y(x),'implicit')

Maple raw output

_C1+((-3*a)^(1/3)*x*AiryAi((-3*a)^(2/3)*x^2+1/(-3*a)^(1/3)/y(x))+AiryAi(1,(-3*a)
^(2/3)*x^2+1/(-3*a)^(1/3)/y(x)))/((-3*a)^(1/3)*x*AiryBi((-3*a)^(2/3)*x^2+1/(-3*a
)^(1/3)/y(x))+AiryBi(1,(-3*a)^(2/3)*x^2+1/(-3*a)^(1/3)/y(x))) = 0