Internal problem ID [1645]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 1.2. Page 6
Problem number: Example 4.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }+y \,{\mathrm e}^{t^{2}}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 19
dsolve([diff(y(t),t)+exp(t^2)*y(t)=0,y(1) = 2],y(t), singsol=all)
\[ y \relax (t ) = 2 \,{\mathrm e}^{\frac {\left (\erfi \relax (1)-\erfi \relax (t )\right ) \sqrt {\pi }}{2}} \]
✓ Solution by Mathematica
Time used: 0.068 (sec). Leaf size: 23
DSolve[{y'[t]+Exp[t^2]*y[t]==0,y[1]==2},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to 2 e^{e F(1)-e^{t^2} F(t)} \\ \end{align*}