Internal problem ID [13030]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 5. LINEAR FIRST ORDER EQUATIONS. Additional exercises. page
103
Problem number: 5.1 (d).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
\[ \boxed {y^{\prime }-\left (x y+3 y\right )^{2}=1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 55
dsolve(diff(y(x),x)=1+(x*y(x)+3*y(x))^2,y(x), singsol=all)
\[ y = -\frac {\operatorname {BesselY}\left (-\frac {1}{4}, \frac {\left (x +3\right )^{2}}{2}\right ) c_{1} +\operatorname {BesselJ}\left (-\frac {1}{4}, \frac {\left (x +3\right )^{2}}{2}\right )}{\left (\operatorname {BesselY}\left (\frac {3}{4}, \frac {\left (x +3\right )^{2}}{2}\right ) c_{1} +\operatorname {BesselJ}\left (\frac {3}{4}, \frac {\left (x +3\right )^{2}}{2}\right )\right ) \left (x +3\right )} \]
✓ Solution by Mathematica
Time used: 0.45 (sec). Leaf size: 351
DSolve[y'[x]==1+(x*y[x]+3*y[x])^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\left ((x+3)^3\right )^{2/3} \operatorname {Gamma}\left (\frac {7}{4}\right ) \operatorname {BesselJ}\left (-\frac {1}{4},\frac {1}{2} \left ((x+3)^3\right )^{2/3}\right )+3 \operatorname {Gamma}\left (\frac {7}{4}\right ) \operatorname {BesselJ}\left (\frac {3}{4},\frac {1}{2} \left ((x+3)^3\right )^{2/3}\right )-\left ((x+3)^3\right )^{2/3} \operatorname {Gamma}\left (\frac {7}{4}\right ) \operatorname {BesselJ}\left (\frac {7}{4},\frac {1}{2} \left ((x+3)^3\right )^{2/3}\right )+4 c_1 \left ((x+3)^3\right )^{2/3} \operatorname {Gamma}\left (\frac {5}{4}\right ) \operatorname {BesselJ}\left (-\frac {7}{4},\frac {1}{2} \left ((x+3)^3\right )^{2/3}\right )+12 c_1 \operatorname {Gamma}\left (\frac {5}{4}\right ) \operatorname {BesselJ}\left (-\frac {3}{4},\frac {1}{2} \left ((x+3)^3\right )^{2/3}\right )-4 c_1 \left ((x+3)^3\right )^{2/3} \operatorname {Gamma}\left (\frac {5}{4}\right ) \operatorname {BesselJ}\left (\frac {1}{4},\frac {1}{2} \left ((x+3)^3\right )^{2/3}\right )}{2 (x+3)^3 \left (\operatorname {Gamma}\left (\frac {7}{4}\right ) \operatorname {BesselJ}\left (\frac {3}{4},\frac {1}{2} \left ((x+3)^3\right )^{2/3}\right )+4 c_1 \operatorname {Gamma}\left (\frac {5}{4}\right ) \operatorname {BesselJ}\left (-\frac {3}{4},\frac {1}{2} \left ((x+3)^3\right )^{2/3}\right )\right )} y(x)\to \frac {-\left ((x+3)^3\right )^{2/3} \operatorname {BesselJ}\left (-\frac {7}{4},\frac {1}{2} \left ((x+3)^3\right )^{2/3}\right )-3 \operatorname {BesselJ}\left (-\frac {3}{4},\frac {1}{2} \left ((x+3)^3\right )^{2/3}\right )+\left ((x+3)^3\right )^{2/3} \operatorname {BesselJ}\left (\frac {1}{4},\frac {1}{2} \left ((x+3)^3\right )^{2/3}\right )}{2 (x+3)^3 \operatorname {BesselJ}\left (-\frac {3}{4},\frac {1}{2} \left ((x+3)^3\right )^{2/3}\right )} \end{align*}