Internal problem ID [12793]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 5. The Laplace Transform Method. Exercises 5.2, page 248
Problem number: 9.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y^{\prime }-y=2 \,{\mathrm e}^{x}} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 5.094 (sec). Leaf size: 12
dsolve([diff(y(x),x)-y(x)=2*exp(x),y(0) = 1],y(x), singsol=all)
\[ y \left (x \right ) = \left (2 x +1\right ) {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.067 (sec). Leaf size: 14
DSolve[{y'[x]-y[x]==2*Exp[x],{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^x (2 x+1) \]