Internal problem ID [15247]
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. Trial and error method. Exercises page 132
Problem number: 477.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {y^{\prime \prime }+7 y^{\prime }={\mathrm e}^{-7 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve(diff(y(x),x$2)+7*diff(y(x),x)=exp(-7*x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (-7 x -7 c_{1} -1\right ) {\mathrm e}^{-7 x}}{49}+c_{2} \]
✓ Solution by Mathematica
Time used: 0.077 (sec). Leaf size: 26
DSolve[y''[x]+7*y'[x]==Exp[-7*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_2-\frac {1}{49} e^{-7 x} (7 x+1+7 c_1) \]