Internal problem ID [13032]
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. Review Exercises for chapter 1. page
136
Problem number: 5.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-\frac {\left (t^{2}-4\right ) \left (y+1\right ) {\mathrm e}^{y}}{\left (t -1\right ) \left (3-y\right )}=0} \]
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 38
dsolve(diff(y(t),t)=( (t^2-4)*(1+y(t))*exp(y(t)))/( (t-1)*(3-y(t))),y(t), singsol=all)
\[ y \left (t \right ) = -\operatorname {RootOf}\left (8 \,{\mathrm e} \,\operatorname {expIntegral}_{1}\left (1-\textit {\_Z} \right )+t^{2}-2 \,{\mathrm e}^{\textit {\_Z}}-6 \ln \left (t -1\right )+2 c_{1} +2 t \right ) \]
✓ Solution by Mathematica
Time used: 1.486 (sec). Leaf size: 53
DSolve[y'[t]==( (t^2-4)*(1+y[t])*Exp[y[t]])/( (t-1)*(3-y[t])),y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \text {InverseFunction}\left [-4 e \operatorname {ExpIntegralEi}(-\text {$\#$1}-1)-e^{-\text {$\#$1}}\&\right ]\left [-\frac {t^2}{2}-t+3 \log (t-1)+\frac {3}{2}+c_1\right ] \\ y(t)\to -1 \\ \end{align*}