Internal problem ID [11408]
Book: A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag,
NY. 2015.
Section: Chapter 1, First order differential equations. Section 1.3.1 Separable equations. Exercises
page 26
Problem number: 28.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }+y^{2} {\mathrm e}^{-t^{2}}=0} \] With initial conditions \begin {align*} \left [y \left (0\right ) = {\frac {1}{2}}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 16
dsolve([diff(y(t),t)=-y(t)^2*exp(-t^2),y(0) = 1/2],y(t), singsol=all)
\[ y \left (t \right ) = \frac {2}{4+\sqrt {\pi }\, \operatorname {erf}\left (t \right )} \]
✓ Solution by Mathematica
Time used: 0.365 (sec). Leaf size: 19
DSolve[{y'[t]==-y[t]^2*Exp[-t^2],{y[0]==1/2}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {2}{\sqrt {\pi } \text {erf}(t)+4} \]