Internal problem ID [12919]
Book: DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th
edition. Brooks/Cole. Boston, USA. 2012
Section: Chapter 1. First-Order Differential Equations. Exercises section 1.3 page 47
Problem number: 16 (v).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-t y-t y^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
dsolve(diff(y(t),t)=t*y(t)+t*y(t)^2,y(t), singsol=all)
\[ y \left (t \right ) = \frac {1}{-1+{\mathrm e}^{-\frac {t^{2}}{2}} c_{1}} \]
✓ Solution by Mathematica
Time used: 0.396 (sec). Leaf size: 45
DSolve[y'[t]==t*y[t]+t*y[t]^2,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -\frac {e^{\frac {t^2}{2}+c_1}}{-1+e^{\frac {t^2}{2}+c_1}} \\ y(t)\to -1 \\ y(t)\to 0 \\ \end{align*}