Internal problem ID [12997]
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: 8.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y^{\prime }-2 y=3 \,{\mathrm e}^{-2 t}} \] With initial conditions \begin {align*} [y \left (0\right ) = 10] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve([diff(y(t),t)-2*y(t)=3*exp(-2*t),y(0) = 10],y(t), singsol=all)
\[ y \left (t \right ) = \frac {43 \,{\mathrm e}^{2 t}}{4}-\frac {3 \,{\mathrm e}^{-2 t}}{4} \]
✓ Solution by Mathematica
Time used: 0.096 (sec). Leaf size: 23
DSolve[{y'[t]-2*y[t]==3*Exp[-2*t],{y[0]==10}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{4} e^{-2 t} \left (43 e^{4 t}-3\right ) \]