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]
Solve \begin {gather*} \boxed {-2 y t +y^{\prime }-1=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.011 (sec). Leaf size: 18
dsolve([-2*t*y(t)+diff(y(t),t) = 1,y(0) = 1],y(t), singsol=all)
\[ y \relax (t ) = \frac {\left (\sqrt {\pi }\, \erf \relax (t )+2\right ) {\mathrm e}^{t^{2}}}{2} \]
✓ 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]
\begin{align*} y(t)\to \frac {1}{2} e^{t^2} \left (\sqrt {\pi } \text {Erf}(t)+2\right ) \\ \end{align*}