Internal problem ID [13810]
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: 6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
\[ \boxed {y^{\prime }+t y^{2}=4 t^{2}} \] With initial conditions \begin {align*} [y \left (2\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 127
dsolve([diff(y(t),t)=4*t^2-t*y(t)^2,y(2) = 1],y(t), singsol=all)
\[ y = -\frac {2 \left (\left (2 \sqrt {2}\, \operatorname {BesselK}\left (\frac {3}{5}, \frac {16 \sqrt {2}}{5}\right )+\operatorname {BesselK}\left (\frac {2}{5}, \frac {16 \sqrt {2}}{5}\right )\right ) \operatorname {BesselI}\left (-\frac {3}{5}, \frac {4 t^{\frac {5}{2}}}{5}\right )+\operatorname {BesselK}\left (\frac {3}{5}, \frac {4 t^{\frac {5}{2}}}{5}\right ) \left (-2 \sqrt {2}\, \operatorname {BesselI}\left (-\frac {3}{5}, \frac {16 \sqrt {2}}{5}\right )+\operatorname {BesselI}\left (\frac {2}{5}, \frac {16 \sqrt {2}}{5}\right )\right )\right ) \sqrt {t}}{\left (-2 \sqrt {2}\, \operatorname {BesselK}\left (\frac {3}{5}, \frac {16 \sqrt {2}}{5}\right )-\operatorname {BesselK}\left (\frac {2}{5}, \frac {16 \sqrt {2}}{5}\right )\right ) \operatorname {BesselI}\left (\frac {2}{5}, \frac {4 t^{\frac {5}{2}}}{5}\right )+\operatorname {BesselK}\left (\frac {2}{5}, \frac {4 t^{\frac {5}{2}}}{5}\right ) \left (-2 \sqrt {2}\, \operatorname {BesselI}\left (-\frac {3}{5}, \frac {16 \sqrt {2}}{5}\right )+\operatorname {BesselI}\left (\frac {2}{5}, \frac {16 \sqrt {2}}{5}\right )\right )} \]
✓ Solution by Mathematica
Time used: 0.268 (sec). Leaf size: 709
DSolve[{y'[t]==4*t^2-t*y[t]^2,{y[2]==1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {-3 t^{5/2} \operatorname {BesselI}\left (\frac {2}{5},\frac {16 \sqrt {2}}{5}\right ) \operatorname {BesselI}\left (\frac {3}{5},\frac {4 t^{5/2}}{5}\right )+4 \sqrt {2} t^{5/2} \operatorname {BesselI}\left (-\frac {3}{5},\frac {16 \sqrt {2}}{5}\right ) \operatorname {BesselI}\left (\frac {3}{5},\frac {4 t^{5/2}}{5}\right )-4 \sqrt {2} t^{5/2} \operatorname {BesselI}\left (\frac {3}{5},\frac {16 \sqrt {2}}{5}\right ) \operatorname {BesselI}\left (\frac {7}{5},\frac {4 t^{5/2}}{5}\right )+3 t^{5/2} \operatorname {BesselI}\left (-\frac {2}{5},\frac {16 \sqrt {2}}{5}\right ) \operatorname {BesselI}\left (\frac {7}{5},\frac {4 t^{5/2}}{5}\right )-4 \sqrt {2} t^{5/2} \operatorname {BesselI}\left (-\frac {7}{5},\frac {16 \sqrt {2}}{5}\right ) \operatorname {BesselI}\left (\frac {7}{5},\frac {4 t^{5/2}}{5}\right )+t^{5/2} \left (4 \sqrt {2} \operatorname {BesselI}\left (-\frac {3}{5},\frac {16 \sqrt {2}}{5}\right )-3 \operatorname {BesselI}\left (\frac {2}{5},\frac {16 \sqrt {2}}{5}\right )+4 \sqrt {2} \operatorname {BesselI}\left (\frac {7}{5},\frac {16 \sqrt {2}}{5}\right )\right ) \operatorname {BesselI}\left (-\frac {7}{5},\frac {4 t^{5/2}}{5}\right )+4 \sqrt {2} t^{5/2} \operatorname {BesselI}\left (\frac {7}{5},\frac {16 \sqrt {2}}{5}\right ) \operatorname {BesselI}\left (\frac {3}{5},\frac {4 t^{5/2}}{5}\right )+t^{5/2} \left (-4 \sqrt {2} \operatorname {BesselI}\left (-\frac {7}{5},\frac {16 \sqrt {2}}{5}\right )+3 \operatorname {BesselI}\left (-\frac {2}{5},\frac {16 \sqrt {2}}{5}\right )-4 \sqrt {2} \operatorname {BesselI}\left (\frac {3}{5},\frac {16 \sqrt {2}}{5}\right )\right ) \operatorname {BesselI}\left (-\frac {3}{5},\frac {4 t^{5/2}}{5}\right )+4 \sqrt {2} \operatorname {BesselI}\left (-\frac {3}{5},\frac {16 \sqrt {2}}{5}\right ) \operatorname {BesselI}\left (-\frac {2}{5},\frac {4 t^{5/2}}{5}\right )+3 \operatorname {BesselI}\left (-\frac {2}{5},\frac {16 \sqrt {2}}{5}\right ) \operatorname {BesselI}\left (\frac {2}{5},\frac {4 t^{5/2}}{5}\right )-4 \sqrt {2} \operatorname {BesselI}\left (-\frac {7}{5},\frac {16 \sqrt {2}}{5}\right ) \operatorname {BesselI}\left (\frac {2}{5},\frac {4 t^{5/2}}{5}\right )+4 \sqrt {2} \operatorname {BesselI}\left (\frac {7}{5},\frac {16 \sqrt {2}}{5}\right ) \operatorname {BesselI}\left (-\frac {2}{5},\frac {4 t^{5/2}}{5}\right )-4 \sqrt {2} \operatorname {BesselI}\left (\frac {3}{5},\frac {16 \sqrt {2}}{5}\right ) \operatorname {BesselI}\left (\frac {2}{5},\frac {4 t^{5/2}}{5}\right )-3 \operatorname {BesselI}\left (\frac {2}{5},\frac {16 \sqrt {2}}{5}\right ) \operatorname {BesselI}\left (-\frac {2}{5},\frac {4 t^{5/2}}{5}\right )}{t^2 \left (\left (4 \sqrt {2} \operatorname {BesselI}\left (-\frac {3}{5},\frac {16 \sqrt {2}}{5}\right )-3 \operatorname {BesselI}\left (\frac {2}{5},\frac {16 \sqrt {2}}{5}\right )+4 \sqrt {2} \operatorname {BesselI}\left (\frac {7}{5},\frac {16 \sqrt {2}}{5}\right )\right ) \operatorname {BesselI}\left (-\frac {2}{5},\frac {4 t^{5/2}}{5}\right )+\left (-4 \sqrt {2} \operatorname {BesselI}\left (-\frac {7}{5},\frac {16 \sqrt {2}}{5}\right )+3 \operatorname {BesselI}\left (-\frac {2}{5},\frac {16 \sqrt {2}}{5}\right )-4 \sqrt {2} \operatorname {BesselI}\left (\frac {3}{5},\frac {16 \sqrt {2}}{5}\right )\right ) \operatorname {BesselI}\left (\frac {2}{5},\frac {4 t^{5/2}}{5}\right )\right )} \]