Internal problem ID [2810]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 3
Problem number: 55.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_Riccati, _special]]
Solve \begin {gather*} \boxed {y^{\prime }-a x -b y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 59
dsolve(diff(y(x),x) = a*x+b*y(x)^2,y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (a b \right )^{\frac {1}{3}} \left (\AiryAi \left (1, -\left (a b \right )^{\frac {1}{3}} x \right ) c_{1}+\AiryBi \left (1, -\left (a b \right )^{\frac {1}{3}} x \right )\right )}{b \left (c_{1} \AiryAi \left (-\left (a b \right )^{\frac {1}{3}} x \right )+\AiryBi \left (-\left (a b \right )^{\frac {1}{3}} x \right )\right )} \]
✓ Solution by Mathematica
Time used: 0.16 (sec). Leaf size: 165
DSolve[y'[x]==a x+b y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sqrt {a} \sqrt {x} \left (-J_{-\frac {2}{3}}\left (\frac {2}{3} \sqrt {a} \sqrt {b} x^{3/2}\right )+c_1 J_{\frac {2}{3}}\left (\frac {2}{3} \sqrt {a} \sqrt {b} x^{3/2}\right )\right )}{\sqrt {b} \left (J_{\frac {1}{3}}\left (\frac {2}{3} \sqrt {a} \sqrt {b} x^{3/2}\right )+c_1 J_{-\frac {1}{3}}\left (\frac {2}{3} \sqrt {a} \sqrt {b} x^{3/2}\right )\right )} \\ y(x)\to \frac {a x^2 \, _0\tilde {F}_1\left (;\frac {5}{3};-\frac {1}{9} a b x^3\right )}{3 \, _0\tilde {F}_1\left (;\frac {2}{3};-\frac {1}{9} a b x^3\right )} \\ \end{align*}