Internal problem ID [4694]
Book: Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill
2014
Section: Chapter 24. Solutions of linear DE by Laplace transforms. Supplementary Problems. page
248
Problem number: Problem 24.19.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, class A]]
Solve \begin {gather*} \boxed {y^{\prime }+2 y-{\mathrm e}^{x}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 15
dsolve([diff(y(x),x)+2*y(x)=exp(x),y(0) = 1],y(x), singsol=all)
\[ y \relax (x ) = \frac {\left ({\mathrm e}^{3 x}+2\right ) {\mathrm e}^{-2 x}}{3} \]
✓ Solution by Mathematica
Time used: 0.07 (sec). Leaf size: 21
DSolve[{y'[x]+2*y[x]==Exp[x],{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{3} e^{-2 x} \left (e^{3 x}+2\right ) \\ \end{align*}