Internal problem ID [2808]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 2
Problem number: 53.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
Solve \begin {gather*} \boxed {y^{\prime }-3 a -3 b x -3 b y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.011 (sec). Leaf size: 80
dsolve(diff(y(x),x) = 3*a+3*b*x+3*b*y(x)^2,y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (\AiryAi \left (1, -\frac {3^{\frac {2}{3}} \left (b x +a \right )}{b^{\frac {1}{3}}}\right ) c_{1}+\AiryBi \left (1, -\frac {3^{\frac {2}{3}} \left (b x +a \right )}{b^{\frac {1}{3}}}\right )\right ) 3^{\frac {2}{3}}}{b^{\frac {1}{3}} \left (3 c_{1} \AiryAi \left (-\frac {3^{\frac {2}{3}} \left (b x +a \right )}{b^{\frac {1}{3}}}\right )+3 \AiryBi \left (-\frac {3^{\frac {2}{3}} \left (b x +a \right )}{b^{\frac {1}{3}}}\right )\right )} \]
✓ Solution by Mathematica
Time used: 0.191 (sec). Leaf size: 191
DSolve[y'[x]==3*(a+b*x+ b*y[x]^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} 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 )} \\ y(x)\to \frac {b \text {Ai}'\left (-\frac {3^{2/3} b (a+b x)}{\left (-b^2\right )^{2/3}}\right )}{\sqrt [3]{3} \left (-b^2\right )^{2/3} \text {Ai}\left (-\frac {3^{2/3} b (a+b x)}{\left (-b^2\right )^{2/3}}\right )} \\ \end{align*}