Internal problem ID [11987]
Book: AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C.
ROBINSON. Cambridge University Press 2004
Section: Chapter 8, Separable equations. Exercises page 72
Problem number: 8.1 (v).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-y^{2} {\mathrm e}^{-t^{2}}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve(diff(y(t),t)=exp(-t^2)*y(t)^2,y(t), singsol=all)
\[ y \left (t \right ) = -\frac {2}{\sqrt {\pi }\, \operatorname {erf}\left (t \right )-2 c_{1}} \]
✓ Solution by Mathematica
Time used: 0.347 (sec). Leaf size: 27
DSolve[y'[t]==Exp[-t^2]*y[t]^2,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -\frac {2}{\sqrt {\pi } \text {erf}(t)+2 c_1} \\ y(t)\to 0 \\ \end{align*}