Internal problem ID [2657]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth
edition, 2015
Section: Chapter 1, First-Order Differential Equations. Section 1.6, First-Order Linear Differential
Equations. page 59
Problem number: Problem 19.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y^{\prime }+y={\mathrm e}^{x}} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 15
dsolve([y(x)-exp(x)+diff(y(x),x)=0,y(0) = 1],y(x), singsol=all)
\[ y \left (x \right ) = \frac {{\mathrm e}^{x}}{2}+\frac {{\mathrm e}^{-x}}{2} \]
✓ Solution by Mathematica
Time used: 0.039 (sec). Leaf size: 21
DSolve[{y[x]-Exp[x]+y'[x]==0,{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} e^{-x} \left (e^{2 x}+1\right ) \]