17.2.6 problem 1.1-3 (f)

Internal problem ID [3430]
Book : Ordinary Differential Equations, Robert H. Martin, 1983
Section : Problem 1.1-3, page 6
Problem number : 1.1-3 (f)
Date solved : Monday, January 27, 2025 at 07:36:26 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=8 \,{\mathrm e}^{4 t}+t \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=12 \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 17

dsolve([diff(y(t),t)=8*exp(4*t)+t,y(0) = 12],y(t), singsol=all)
 

\[ y = \frac {t^{2}}{2}+2 \,{\mathrm e}^{4 t}+10 \]

✓ Solution by Mathematica

Time used: 0.009 (sec). Leaf size: 21

DSolve[{D[y[t],t]==8*Exp[4*t]+t,y[0]==12},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{2} \left (t^2+4 e^{4 t}+20\right ) \]