Internal problem ID [1661]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 1.2. Page 9
Problem number: 14.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }-2 t y=1} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve([-2*t*y(t)+diff(y(t),t) = 1,y(0) = 1],y(t), singsol=all)
\[ y \left (t \right ) = \frac {\left (\sqrt {\pi }\, \operatorname {erf}\left (t \right )+2\right ) {\mathrm e}^{t^{2}}}{2} \]
✓ Solution by Mathematica
Time used: 0.038 (sec). Leaf size: 24
DSolve[{-2*t*y[t]+y'[t] == 1,y[0]==1},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{2} e^{t^2} \left (\sqrt {\pi } \text {erf}(t)+2\right ) \]