Internal problem ID [14189]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number: 31.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-t^{2} y^{2}-y^{2}=-t^{2}-1} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 15
dsolve(diff(y(t),t)=t^2*y(t)^2+y(t)^2-t^2-1,y(t), singsol=all)
\[ y \left (t \right ) = -\tanh \left (\frac {1}{3} t^{3}+c_{1} +t \right ) \]
✓ Solution by Mathematica
Time used: 0.287 (sec). Leaf size: 58
DSolve[y'[t]==t^2*y[t]^2+y[t]^2-t^2-1,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1-e^{\frac {2 t^3}{3}+2 t+2 c_1}}{1+e^{\frac {2 t^3}{3}+2 t+2 c_1}} \\ y(t)\to -1 \\ y(t)\to 1 \\ \end{align*}