##### 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 = 0.623128 (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 = 0.07 (sec), leaf count = 48

$\left [y \left (x \right ) = \frac {1}{3 a \,x^{2}+\RootOf \left (\left (-3 a \right )^{\frac {1}{3}} \AiryBi \left (\textit {\_Z} \right ) \textit {\_C1} x +\left (-3 a \right )^{\frac {1}{3}} x \AiryAi \left (\textit {\_Z} \right )+\AiryBi \left (1, \textit {\_Z}\right ) \textit {\_C1} +\AiryAi \left (1, \textit {\_Z}\right )\right ) \left (-3 a \right )^{\frac {1}{3}}}\right ]$ 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))

Maple raw output

[y(x) = 1/(3*a*x^2+RootOf((-3*a)^(1/3)*AiryBi(_Z)*_C1*x+(-3*a)^(1/3)*x*AiryAi(_Z
)+AiryBi(1,_Z)*_C1+AiryAi(1,_Z))*(-3*a)^(1/3))]