Internal problem ID [1950]
Book: Ordinary Differential Equations, Robert H. Martin, 1983
Section: Problem 1.1-3, page 6
Problem number: 1.1-3 (f).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }-8 \,{\mathrm e}^{4 t}-t=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 12] \end {align*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 17
dsolve([diff(y(t),t)=8*exp(4*t)+t,y(0) = 12],y(t), singsol=all)
\[ y \relax (t ) = \frac {t^{2}}{2}+2 \,{\mathrm e}^{4 t}+10 \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 21
DSolve[{y'[t]==8*Exp[4*t]+t,y[0]==12},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{2} \left (t^2+4 e^{4 t}+20\right ) \\ \end{align*}