Internal problem ID [12635]
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 1.6 page 89
Problem number: 2 and 14(i).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }-y^{2}+4 y=-12} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 23
dsolve([diff(y(t),t)=y(t)^2-4*y(t)-12,y(0) = 1],y(t), singsol=all)
\[ y \left (t \right ) = \frac {-10 \,{\mathrm e}^{8 t}+18}{5 \,{\mathrm e}^{8 t}+3} \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 26
DSolve[{y'[t]==y[t]^2-4*y[t]-12,{y[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {18-10 e^{8 t}}{5 e^{8 t}+3} \]