Internal problem ID [3317]
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]
\[ \boxed {y^{\prime }-3 b y^{2}=3 b x +3 a} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 80
dsolve(diff(y(x),x) = 3*a+3*b*x+3*b*y(x)^2,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (\operatorname {AiryAi}\left (1, -\frac {3^{\frac {2}{3}} \left (x b +a \right )}{b^{\frac {1}{3}}}\right ) c_{1} +\operatorname {AiryBi}\left (1, -\frac {3^{\frac {2}{3}} \left (x b +a \right )}{b^{\frac {1}{3}}}\right )\right ) 3^{\frac {2}{3}}}{b^{\frac {1}{3}} \left (3 c_{1} \operatorname {AiryAi}\left (-\frac {3^{\frac {2}{3}} \left (x b +a \right )}{b^{\frac {1}{3}}}\right )+3 \operatorname {AiryBi}\left (-\frac {3^{\frac {2}{3}} \left (x b +a \right )}{b^{\frac {1}{3}}}\right )\right )} \]
✓ Solution by Mathematica
Time used: 0.219 (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 (\operatorname {AiryBiPrime}\left (-\frac {3^{2/3} b (a+b x)}{\left (-b^2\right )^{2/3}}\right )+c_1 \operatorname {AiryAiPrime}\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 (\operatorname {AiryBi}\left (-\frac {3^{2/3} b (a+b x)}{\left (-b^2\right )^{2/3}}\right )+c_1 \operatorname {AiryAi}\left (-\frac {3^{2/3} b (a+b x)}{\left (-b^2\right )^{2/3}}\right )\right )} y(x)\to \frac {b \operatorname {AiryAiPrime}\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} \operatorname {AiryAi}\left (-\frac {3^{2/3} b (a+b x)}{\left (-b^2\right )^{2/3}}\right )} \end{align*}