1.2 problem Example 4

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]

\[ \boxed {y^{\prime }+y \,{\mathrm e}^{t^{2}}=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 2] \end {align*}

✓ Solution by Maple

Time used: 0.11 (sec). Leaf size: 22

dsolve([diff(y(t),t)+exp(t^2)*y(t)=0,y(1) = 2],y(t), singsol=all)
 

\[ y \left (t \right ) = 2 \,{\mathrm e}^{\frac {\left (\operatorname {erfi}\left (1\right )-\operatorname {erfi}\left (t \right )\right ) \sqrt {\pi }}{2}} \]

✓ Solution by Mathematica

Time used: 0.066 (sec). Leaf size: 25

DSolve[{y'[t]+Exp[t^2]*y[t]==0,y[1]==2},y[t],t,IncludeSingularSolutions -> True]
                                                                                    
                                                                                    
 

\[ y(t)\to 2 e^{\frac {1}{2} \sqrt {\pi } (\text {erfi}(1)-\text {erfi}(t))} \]