Internal problem ID [12588]
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 1.3 page 47
Problem number: 9.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
\[ \boxed {y^{\prime }-\left (y+\frac {1}{2}\right ) \left (t +y\right )=0} \] With initial conditions \begin {align*} \left [y \left (0\right ) = {\frac {1}{2}}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 65
dsolve([diff(y(t),t)=(y(t)+1/2)*(y(t)+t),y(0) = 1/2],y(t), singsol=all)
\[ y \left (t \right ) = \frac {-i \sqrt {\pi }\, {\mathrm e}^{-\frac {1}{8}} \sqrt {2}\, \operatorname {erf}\left (\frac {i \sqrt {2}\, \left (-1+2 t \right )}{4}\right )-i \sqrt {\pi }\, {\mathrm e}^{-\frac {1}{8}} \sqrt {2}\, \operatorname {erf}\left (\frac {i \sqrt {2}}{4}\right )+4 \,{\mathrm e}^{\frac {t \left (t -1\right )}{2}}-2}{2 i \sqrt {\pi }\, {\mathrm e}^{-\frac {1}{8}} \sqrt {2}\, \operatorname {erf}\left (\frac {i \sqrt {2}\, \left (-1+2 t \right )}{4}\right )+2 i \sqrt {\pi }\, {\mathrm e}^{-\frac {1}{8}} \sqrt {2}\, \operatorname {erf}\left (\frac {i \sqrt {2}}{4}\right )+4} \]
✓ Solution by Mathematica
Time used: 0.332 (sec). Leaf size: 124
DSolve[{y'[t]==(y[t]+1/2)*(y[t]+t),{y[0]==1/2}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {-\sqrt {2 \pi } \text {erfi}\left (\frac {1-2 t}{2 \sqrt {2}}\right )+\sqrt {2 \pi } \text {erfi}\left (\frac {1}{2 \sqrt {2}}\right )+4 e^{\frac {1}{8} (1-2 t)^2}-2 \sqrt [8]{e}}{2 \sqrt {2 \pi } \text {erfi}\left (\frac {1-2 t}{2 \sqrt {2}}\right )-2 \sqrt {2 \pi } \text {erfi}\left (\frac {1}{2 \sqrt {2}}\right )+4 \sqrt [8]{e}} \]