17.2.4 problem 1.1-3 (d)

Internal problem ID [3428]
Book : Ordinary Differential Equations, Robert H. Martin, 1983
Section : Problem 1.1-3, page 6
Problem number : 1.1-3 (d)
Date solved : Monday, January 27, 2025 at 07:36:24 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=t \,{\mathrm e}^{2 t} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=5 \end{align*}

✓ Solution by Maple

Time used: 0.036 (sec). Leaf size: 21

dsolve([diff(y(t),t)=t*exp(2*t),y(1) = 5],y(t), singsol=all)
 

\[ y = \frac {\left (2 t -1\right ) {\mathrm e}^{2 t}}{4}+5-\frac {{\mathrm e}^{2}}{4} \]

✓ Solution by Mathematica

Time used: 0.006 (sec). Leaf size: 27

DSolve[{D[y[t],t]==t*Exp[2*t],y[1]==5},y[t],t,IncludeSingularSolutions -> True]
 

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