Internal problem ID [7594]
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]
Solve \begin {gather*} \boxed {y^{\prime }+y^{2}-x a -b=0} \end {gather*}
✓ Solution by Maple
Time used: 0.029 (sec). Leaf size: 79
dsolve(diff(y(x),x) + y(x)^2 - a*x - b=0,y(x), singsol=all)
\[ y \relax (x ) = -\frac {i \left (-i a \right )^{\frac {1}{3}} \left (\AiryAi \left (1, -\frac {a x +b}{\left (-i a \right )^{\frac {2}{3}}}\right ) c_{1}+\AiryBi \left (1, -\frac {a x +b}{\left (-i a \right )^{\frac {2}{3}}}\right )\right )}{\AiryAi \left (-\frac {a x +b}{\left (-i a \right )^{\frac {2}{3}}}\right ) c_{1}+\AiryBi \left (-\frac {a x +b}{\left (-i a \right )^{\frac {2}{3}}}\right )} \]
✓ Solution by Mathematica
Time used: 0.155 (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 {Bi}'\left (\frac {b+a x}{a^{2/3}}\right )+c_1 \operatorname {Ai}'\left (\frac {b+a x}{a^{2/3}}\right )\right )}{\operatorname {Bi}\left (\frac {b+a x}{a^{2/3}}\right )+c_1 \operatorname {Ai}\left (\frac {b+a x}{a^{2/3}}\right )} \\ y(x)\to \frac {\sqrt [3]{a} \operatorname {Ai}'\left (\frac {b+a x}{a^{2/3}}\right )}{\operatorname {Ai}\left (\frac {b+a x}{a^{2/3}}\right )} \\ \end{align*}