Internal problem ID [14570]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.3, page 156
Problem number: 62 (c).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y^{\prime }-y={\mathrm e}^{4 t}} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 14
dsolve([diff(y(t),t)-y(t)=exp(4*t),y(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = \frac {\left ({\mathrm e}^{3 t}-1\right ) {\mathrm e}^{t}}{3} \]
✓ Solution by Mathematica
Time used: 0.042 (sec). Leaf size: 19
DSolve[{y'[t]-y[t]==Exp[4*t],{y[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{3} e^t \left (e^{3 t}-1\right ) \]