Internal problem ID [1948]
Book: Ordinary Differential Equations, Robert H. Martin, 1983
Section: Problem 1.1-3, page 6
Problem number: 1.1-3 (d).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }-{\mathrm e}^{2 t} t=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 5] \end {align*}
✓ Solution by Maple
Time used: 0.019 (sec). Leaf size: 21
dsolve([diff(y(t),t)=t*exp(2*t),y(1) = 5],y(t), singsol=all)
\[ y \relax (t ) = \frac {\left (2 t -1\right ) {\mathrm e}^{2 t}}{4}+5-\frac {{\mathrm e}^{2}}{4} \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 27
DSolve[{y'[t]==t*Exp[2*t],y[1]==5},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{4} \left (e^{2 t} (2 t-1)-e^2+20\right ) \\ \end{align*}