Internal problem ID [2811]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 3
Problem number: 56.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
Solve \begin {gather*} \boxed {y^{\prime }-a -b x -c y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 85
dsolve(diff(y(x),x) = a+b*x+c*y(x)^2,y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (\frac {b}{\sqrt {c}}\right )^{\frac {1}{3}} \left (\AiryAi \left (1, -\frac {b x +a}{\left (\frac {b}{\sqrt {c}}\right )^{\frac {2}{3}}}\right ) c_{1}+\AiryBi \left (1, -\frac {b x +a}{\left (\frac {b}{\sqrt {c}}\right )^{\frac {2}{3}}}\right )\right )}{\sqrt {c}\, \left (c_{1} \AiryAi \left (-\frac {b x +a}{\left (\frac {b}{\sqrt {c}}\right )^{\frac {2}{3}}}\right )+\AiryBi \left (-\frac {b x +a}{\left (\frac {b}{\sqrt {c}}\right )^{\frac {2}{3}}}\right )\right )} \]
✓ Solution by Mathematica
Time used: 0.191 (sec). Leaf size: 143
DSolve[y'[x]==a+b x+c y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {b \left (\text {Bi}'\left (-\frac {c (a+b x)}{(-b c)^{2/3}}\right )+c_1 \text {Ai}'\left (-\frac {c (a+b x)}{(-b c)^{2/3}}\right )\right )}{(-b c)^{2/3} \left (\text {Bi}\left (-\frac {c (a+b x)}{(-b c)^{2/3}}\right )+c_1 \text {Ai}\left (-\frac {c (a+b x)}{(-b c)^{2/3}}\right )\right )} \\ y(x)\to \frac {b \text {Ai}'\left (-\frac {c (a+b x)}{(-b c)^{2/3}}\right )}{(-b c)^{2/3} \text {Ai}\left (-\frac {c (a+b x)}{(-b c)^{2/3}}\right )} \\ \end{align*}