Internal problem ID [14125]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.1, page 32
Problem number: 1 (a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
\[ \boxed {y^{\prime }-y^{2}=-t^{2}} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.859 (sec). Leaf size: 59
dsolve([diff(y(t),t)+t^2=y(t)^2,y(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = -\left (\left \{\begin {array}{cc} 0 & t =0 \\ \frac {\left (\operatorname {BesselI}\left (-\frac {3}{4}, \frac {t^{2}}{2}\right ) \pi \sqrt {2}-2 \operatorname {BesselK}\left (\frac {3}{4}, \frac {t^{2}}{2}\right )\right ) t}{\pi \sqrt {2}\, \operatorname {BesselI}\left (\frac {1}{4}, \frac {t^{2}}{2}\right )+2 \operatorname {BesselK}\left (\frac {1}{4}, \frac {t^{2}}{2}\right )} & \operatorname {otherwise} \end {array}\right .\right ) \]
✓ Solution by Mathematica
Time used: 0.663 (sec). Leaf size: 81
DSolve[{y'[t]+t^2==y[t]^2,{y[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to -\frac {i t^2 \operatorname {BesselJ}\left (-\frac {5}{4},\frac {i t^2}{2}\right )-i t^2 \operatorname {BesselJ}\left (\frac {3}{4},\frac {i t^2}{2}\right )+\operatorname {BesselJ}\left (-\frac {1}{4},\frac {i t^2}{2}\right )}{2 t \operatorname {BesselJ}\left (-\frac {1}{4},\frac {i t^2}{2}\right )} \]