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]
Solve \begin {gather*} \boxed {y t +y^{\prime }-t -1=0} \end {gather*} With initial conditions \begin {align*} \left [y \left (\frac {3}{2}\right ) = 0\right ] \end {align*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 48
dsolve([t*y(t)+diff(y(t),t) = 1+t,y(3/2) = 0],y(t), singsol=all)
\[ y \relax (t ) = -\frac {\sqrt {2}\, \sqrt {\pi }\, \left (i \erf \left (\frac {i \sqrt {2}\, t}{2}\right )+\erfi \left (\frac {3 \sqrt {2}}{4}\right )\right ) {\mathrm e}^{-\frac {t^{2}}{2}}}{2}-{\mathrm e}^{\frac {9}{8}-\frac {t^{2}}{2}}+1 \]
✓ Solution by Mathematica
Time used: 0.089 (sec). Leaf size: 54
DSolve[{t*y[t]+y'[t] == 1+t,y[3/2]==0},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -\left (\sqrt {2} F\left (\frac {3}{2 \sqrt {2}}\right )+1\right ) e^{\frac {9}{8}-\frac {t^2}{2}}+\sqrt {2} F\left (\frac {t}{\sqrt {2}}\right )+1 \\ \end{align*}