Internal problem ID [6593]
Book: First order enumerated odes
Section: section 1
Problem number: 30.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
Solve \begin {gather*} \boxed {y^{\prime }-x -y-b y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.013 (sec). Leaf size: 105
dsolve(diff(y(x),x)=x+y(x)+b*y(x)^2,y(x), singsol=all)
\[ y \relax (x ) = \frac {2 b^{\frac {1}{3}} \AiryAi \left (1, -\frac {4 b x -1}{4 b^{\frac {2}{3}}}\right ) c_{1}+2 \AiryBi \left (1, -\frac {4 b x -1}{4 b^{\frac {2}{3}}}\right ) b^{\frac {1}{3}}-\AiryAi \left (-\frac {4 b x -1}{4 b^{\frac {2}{3}}}\right ) c_{1}-\AiryBi \left (-\frac {4 b x -1}{4 b^{\frac {2}{3}}}\right )}{2 b \left (\AiryAi \left (-\frac {4 b x -1}{4 b^{\frac {2}{3}}}\right ) c_{1}+\AiryBi \left (-\frac {4 b x -1}{4 b^{\frac {2}{3}}}\right )\right )} \]
✓ Solution by Mathematica
Time used: 0.178 (sec). Leaf size: 195
DSolve[y'[x]==x+y[x]+b*y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\text {Bi}\left (\frac {\frac {1}{4}-b x}{(-b)^{2/3}}\right )+c_1 \text {Ai}\left (\frac {\frac {1}{4}-b x}{(-b)^{2/3}}\right )+2 \sqrt [3]{-b} \left (\text {Bi}'\left (\frac {\frac {1}{4}-b x}{(-b)^{2/3}}\right )+c_1 \text {Ai}'\left (\frac {\frac {1}{4}-b x}{(-b)^{2/3}}\right )\right )}{2 b \left (\text {Bi}\left (\frac {\frac {1}{4}-b x}{(-b)^{2/3}}\right )+c_1 \text {Ai}\left (\frac {\frac {1}{4}-b x}{(-b)^{2/3}}\right )\right )} \\ y(x)\to -\frac {\frac {2 \sqrt [3]{-b} \text {Ai}'\left (\frac {\frac {1}{4}-b x}{(-b)^{2/3}}\right )}{\text {Ai}\left (\frac {\frac {1}{4}-b x}{(-b)^{2/3}}\right )}+1}{2 b} \\ \end{align*}