Internal problem ID [6592]
Book: First order enumerated odes
Section: section 1
Problem number: 30.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
\[ \boxed {y^{\prime }-x -y-b y^{2}=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 105
dsolve(diff(y(x),x)=x+y(x)+b*y(x)^2,y(x), singsol=all)
\[ y \left (x \right ) = \frac {2 b^{\frac {1}{3}} \operatorname {AiryAi}\left (1, -\frac {4 x b -1}{4 b^{\frac {2}{3}}}\right ) c_{1} +2 \operatorname {AiryBi}\left (1, -\frac {4 x b -1}{4 b^{\frac {2}{3}}}\right ) b^{\frac {1}{3}}-\operatorname {AiryAi}\left (-\frac {4 x b -1}{4 b^{\frac {2}{3}}}\right ) c_{1} -\operatorname {AiryBi}\left (-\frac {4 x b -1}{4 b^{\frac {2}{3}}}\right )}{2 b \left (\operatorname {AiryAi}\left (-\frac {4 x b -1}{4 b^{\frac {2}{3}}}\right ) c_{1} +\operatorname {AiryBi}\left (-\frac {4 x b -1}{4 b^{\frac {2}{3}}}\right )\right )} \]
✓ Solution by Mathematica
Time used: 0.175 (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 {\operatorname {AiryBi}\left (\frac {\frac {1}{4}-b x}{(-b)^{2/3}}\right )+c_1 \operatorname {AiryAi}\left (\frac {\frac {1}{4}-b x}{(-b)^{2/3}}\right )+2 \sqrt [3]{-b} \left (\operatorname {AiryBiPrime}\left (\frac {\frac {1}{4}-b x}{(-b)^{2/3}}\right )+c_1 \operatorname {AiryAiPrime}\left (\frac {\frac {1}{4}-b x}{(-b)^{2/3}}\right )\right )}{2 b \left (\operatorname {AiryBi}\left (\frac {\frac {1}{4}-b x}{(-b)^{2/3}}\right )+c_1 \operatorname {AiryAi}\left (\frac {\frac {1}{4}-b x}{(-b)^{2/3}}\right )\right )} \\ y(x)\to -\frac {\frac {2 \sqrt [3]{-b} \operatorname {AiryAiPrime}\left (\frac {\frac {1}{4}-b x}{(-b)^{2/3}}\right )}{\operatorname {AiryAi}\left (\frac {\frac {1}{4}-b x}{(-b)^{2/3}}\right )}+1}{2 b} \\ \end{align*}