Internal problem ID [11657]
Book: AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C.
ROBINSON. Cambridge University Press 2004
Section: Chapter 5, Trivial differential equations. Exercises page 33
Problem number: 5.4 (v).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {3 \,{\mathrm e}^{3 t} x+{\mathrm e}^{3 t} x^{\prime }={\mathrm e}^{-t}} \] With initial conditions \begin {align*} [x \left (0\right ) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 16
dsolve([diff(x(t)*exp(3*t),t)=exp(-t),x(0) = 3],x(t), singsol=all)
\[ x \left (t \right ) = -\left ({\mathrm e}^{-t}-4\right ) {\mathrm e}^{-3 t} \]
✓ Solution by Mathematica
Time used: 0.092 (sec). Leaf size: 18
DSolve[{D[x[t]*Exp[3*t],t]==Exp[-t],{x[0]==3}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to e^{-4 t} \left (4 e^t-1\right ) \]