Internal problem ID [1659]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 1.2. Page 9
Problem number: 12.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y t +y^{\prime }=t +1} \] With initial conditions \begin {align*} \left [y \left (\frac {3}{2}\right ) = 0\right ] \end {align*}
✓ Solution by Maple
Time used: 0.125 (sec). Leaf size: 50
dsolve([t*y(t)+diff(y(t),t) = 1+t,y(3/2) = 0],y(t), singsol=all)
\[ y \left (t \right ) = 1-{\mathrm e}^{\frac {9}{8}-\frac {t^{2}}{2}}+\frac {\sqrt {2}\, \sqrt {\pi }\, \left (-i \operatorname {erf}\left (\frac {i \sqrt {2}\, t}{2}\right )-\operatorname {erfi}\left (\frac {3 \sqrt {2}}{4}\right )\right ) {\mathrm e}^{-\frac {t^{2}}{2}}}{2} \]
✓ Solution by Mathematica
Time used: 0.088 (sec). Leaf size: 72
DSolve[{t*y[t]+y'[t] == 1+t,y[3/2]==0},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{2} e^{-\frac {t^2}{2}} \left (\sqrt {2 \pi } \text {erfi}\left (\frac {t}{\sqrt {2}}\right )-\sqrt {2 \pi } \text {erfi}\left (\frac {3}{2 \sqrt {2}}\right )+2 e^{\frac {t^2}{2}}-2 e^{9/8}\right ) \]