Internal problem ID [15364]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 15.3 Nonhomogeneous linear equations with
constant coefficients. Initial value problem. Exercises page 140
Problem number: 595.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {y^{\prime \prime }+y^{\prime }={\mathrm e}^{-x}} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 13
dsolve([diff(y(x),x$2)+diff(y(x),x)=exp(-x),y(0) = 1, D(y)(0) = -1],y(x), singsol=all)
\[ y \left (x \right ) = -{\mathrm e}^{-x} x +1 \]
✓ Solution by Mathematica
Time used: 0.069 (sec). Leaf size: 15
DSolve[{y''[x]+y'[x]==Exp[-x],{y[0]==1,y'[0]==-1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 1-e^{-x} x \]