Internal problem ID [1714]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.1, second order linear differential equations. Page 134
Problem number: 6(a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
\[ \boxed {y^{\prime \prime }+t y^{\prime }+y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 33
dsolve(diff(y(t),t$2)+t*diff(y(t),t)+y(t)=0,y(t), singsol=all)
\[ y \left (t \right ) = \operatorname {erf}\left (\frac {i \sqrt {2}\, t}{2}\right ) {\mathrm e}^{-\frac {t^{2}}{2}} c_{1} +c_{2} {\mathrm e}^{-\frac {t^{2}}{2}} \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 34
DSolve[y''[t]+t*y'[t]+y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \sqrt {2} c_1 \operatorname {DawsonF}\left (\frac {t}{\sqrt {2}}\right )+c_2 e^{-\frac {t^2}{2}} \\ \end{align*}