Internal problem ID [12610]
Book: DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th
edition. Brooks/Cole. Boston, USA. 2012
Section: Chapter 1. First-Order Differential Equations. Exercises section 1.4 page 61
Problem number: 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_Riccati, _special]]
\[ \boxed {y^{\prime }+y^{2}=t} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 89
dsolve([diff(y(t),t)=t-y(t)^2,y(0) = 1],y(t), singsol=all)
\[ y \left (t \right ) = \frac {2 \operatorname {AiryAi}\left (1, t\right ) \pi 3^{\frac {5}{6}}-3 \operatorname {AiryAi}\left (1, t\right ) \Gamma \left (\frac {2}{3}\right )^{2} 3^{\frac {2}{3}}-3 \operatorname {AiryBi}\left (1, t\right ) 3^{\frac {1}{6}} \Gamma \left (\frac {2}{3}\right )^{2}-2 \operatorname {AiryBi}\left (1, t\right ) \pi 3^{\frac {1}{3}}}{2 \operatorname {AiryAi}\left (t \right ) \pi 3^{\frac {5}{6}}-3 \operatorname {AiryAi}\left (t \right ) \Gamma \left (\frac {2}{3}\right )^{2} 3^{\frac {2}{3}}-3 \operatorname {AiryBi}\left (t \right ) 3^{\frac {1}{6}} \Gamma \left (\frac {2}{3}\right )^{2}-2 \operatorname {AiryBi}\left (t \right ) \pi 3^{\frac {1}{3}}} \]
✓ Solution by Mathematica
Time used: 11.27 (sec). Leaf size: 163
DSolve[{y'[t]==t-y[t]^2,{y[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {2 i t^{3/2} \operatorname {Gamma}\left (\frac {1}{3}\right ) \operatorname {BesselJ}\left (-\frac {2}{3},\frac {2}{3} i t^{3/2}\right )+\sqrt [3]{-3} \operatorname {Gamma}\left (\frac {2}{3}\right ) \left (i t^{3/2} \operatorname {BesselJ}\left (-\frac {4}{3},\frac {2}{3} i t^{3/2}\right )-i t^{3/2} \operatorname {BesselJ}\left (\frac {2}{3},\frac {2}{3} i t^{3/2}\right )+\operatorname {BesselJ}\left (-\frac {1}{3},\frac {2}{3} i t^{3/2}\right )\right )}{2 t \left (\sqrt [3]{-3} \operatorname {Gamma}\left (\frac {2}{3}\right ) \operatorname {BesselJ}\left (-\frac {1}{3},\frac {2}{3} i t^{3/2}\right )+\operatorname {Gamma}\left (\frac {1}{3}\right ) \operatorname {BesselJ}\left (\frac {1}{3},\frac {2}{3} i t^{3/2}\right )\right )} \]