Internal problem ID [12676]
Book: DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th
edition. Brooks/Cole. Boston, USA. 2012
Section: Chapter 1. First-Order Differential Equations. Exercises section 1.8 page 121
Problem number: 7.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y^{\prime }+2 y={\mathrm e}^{\frac {t}{3}}} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve([diff(y(t),t)+2*y(t)=exp(t/3),y(0) = 1],y(t), singsol=all)
\[ y \left (t \right ) = \frac {\left (3 \,{\mathrm e}^{\frac {7 t}{3}}+4\right ) {\mathrm e}^{-2 t}}{7} \]
✓ Solution by Mathematica
Time used: 0.096 (sec). Leaf size: 25
DSolve[{y'[t]+2*y[t]==Exp[t/3],{y[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{7} e^{-2 t} \left (3 e^{7 t/3}+4\right ) \]