Internal problem ID [6726]
Book: Second order enumerated odes
Section: section 2
Problem number: 41.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_Riccati, _special]]
Solve \begin {gather*} \boxed {y^{\prime }-x +y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 23
dsolve(diff(y(x),x)=x-y(x)^2,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1} \AiryAi \left (1, x\right )+\AiryBi \left (1, x\right )}{c_{1} \AiryAi \relax (x )+\AiryBi \relax (x )} \]
✓ Solution by Mathematica
Time used: 0.116 (sec). Leaf size: 118
DSolve[y'[x]==x-y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {i \sqrt {x} \left (J_{-\frac {2}{3}}\left (\frac {2}{3} i x^{3/2}\right )-c_1 J_{\frac {2}{3}}\left (\frac {2}{3} i x^{3/2}\right )\right )}{J_{\frac {1}{3}}\left (\frac {2}{3} i x^{3/2}\right )+c_1 J_{-\frac {1}{3}}\left (\frac {2}{3} i x^{3/2}\right )} \\ y(x)\to \frac {3 \text {Ai}'(x)+\sqrt {3} \text {Bi}'(x)}{3 \text {Ai}(x)+\sqrt {3} \text {Bi}(x)} \\ \end{align*}