Internal problem ID [15042]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 6. Linear equations of the first order. The Bernoulli equation. Exercises page
54
Problem number: 149.
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 (\infty \right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 8
dsolve([diff(y(x),x)-y(x)=-2*exp(-x),y(infinity) = 0],y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.068 (sec). Leaf size: 10
DSolve[{y'[x]-y[x]==-2*Exp[-x],{y[Infinity]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x} \]