##### 4.2.4 $$y'(x)=3 \left (a+b y(x)^2+b x\right )$$

ODE
$y'(x)=3 \left (a+b y(x)^2+b x\right )$ ODE Classiﬁcation

[_Riccati]

Book solution method
Riccati ODE, Generalized ODE

Mathematica
cpu = 0.261682 (sec), leaf count = 123

$\left \{\left \{y(x)\to \frac {b \left (\text {Bi}'\left (-\frac {3^{2/3} b (a+b x)}{\left (-b^2\right )^{2/3}}\right )+c_1 \text {Ai}'\left (-\frac {3^{2/3} b (a+b x)}{\left (-b^2\right )^{2/3}}\right )\right )}{\sqrt [3]{3} \left (-b^2\right )^{2/3} \left (\text {Bi}\left (-\frac {3^{2/3} b (a+b x)}{\left (-b^2\right )^{2/3}}\right )+c_1 \text {Ai}\left (-\frac {3^{2/3} b (a+b x)}{\left (-b^2\right )^{2/3}}\right )\right )}\right \}\right \}$

Maple
cpu = 0.173 (sec), leaf count = 80

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

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

Mathematica raw output

{{y[x] -> (b*(AiryBiPrime[-((3^(2/3)*b*(a + b*x))/(-b^2)^(2/3))] + AiryAiPrime[-
((3^(2/3)*b*(a + b*x))/(-b^2)^(2/3))]*C[1]))/(3^(1/3)*(-b^2)^(2/3)*(AiryBi[-((3^
(2/3)*b*(a + b*x))/(-b^2)^(2/3))] + AiryAi[-((3^(2/3)*b*(a + b*x))/(-b^2)^(2/3))
]*C[1]))}}

Maple raw input

dsolve(diff(y(x),x) = 3*a+3*b*x+3*b*y(x)^2, y(x))

Maple raw output

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