75.18.6 problem 595

Internal problem ID [17094]
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 ODEs). Section 15.3 Nonhomogeneous linear equations with constant coefficients. Initial value problem. Exercises page 140
Problem number : 595
Date solved : Tuesday, January 28, 2025 at 09:52:10 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} y^{\prime \prime }+y^{\prime }&={\mathrm e}^{-x} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 0.015 (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)
 

\[ y = -x \,{\mathrm e}^{-x}+1 \]

✓ Solution by Mathematica

Time used: 1.655 (sec). Leaf size: 45

DSolve[{D[y[x],{x,2}]+D[y[x],x]==Exp[-x],{y[0]==1,Derivative[1][y][0] ==-1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \int _1^xe^{-K[1]} (K[1]-1)dK[1]-\int _1^0e^{-K[1]} (K[1]-1)dK[1]+1 \]