Internal problem ID [8350]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 13.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
\[ \boxed {y^{\prime }+y^{2}=a x +b} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 79
dsolve(diff(y(x),x) + y(x)^2 - a*x - b=0,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {i \left (-i a \right )^{\frac {1}{3}} \left (\operatorname {AiryAi}\left (1, -\frac {a x +b}{\left (-i a \right )^{\frac {2}{3}}}\right ) c_{1} +\operatorname {AiryBi}\left (1, -\frac {a x +b}{\left (-i a \right )^{\frac {2}{3}}}\right )\right )}{\operatorname {AiryAi}\left (-\frac {a x +b}{\left (-i a \right )^{\frac {2}{3}}}\right ) c_{1} +\operatorname {AiryBi}\left (-\frac {a x +b}{\left (-i a \right )^{\frac {2}{3}}}\right )} \]
✓ Solution by Mathematica
Time used: 0.185 (sec). Leaf size: 105
DSolve[y'[x] + y[x]^2 - a*x - b==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sqrt [3]{a} \left (\operatorname {AiryBiPrime}\left (\frac {b+a x}{a^{2/3}}\right )+c_1 \operatorname {AiryAiPrime}\left (\frac {b+a x}{a^{2/3}}\right )\right )}{\operatorname {AiryBi}\left (\frac {b+a x}{a^{2/3}}\right )+c_1 \operatorname {AiryAi}\left (\frac {b+a x}{a^{2/3}}\right )} y(x)\to \frac {\sqrt [3]{a} \operatorname {AiryAiPrime}\left (\frac {b+a x}{a^{2/3}}\right )}{\operatorname {AiryAi}\left (\frac {b+a x}{a^{2/3}}\right )} \end{align*}