Internal problem ID [15321]
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. Superposition principle. Exercises page 137
Problem number: 552.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {y^{\prime \prime }+4 y^{\prime }=x +{\mathrm e}^{-4 x}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 28
dsolve(diff(y(x),x$2)+4*diff(y(x),x)=x+exp(-4*x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (-4 x -4 c_{1} -1\right ) {\mathrm e}^{-4 x}}{16}+\frac {x^{2}}{8}-\frac {x}{16}+c_{2} \]
✓ Solution by Mathematica
Time used: 0.35 (sec). Leaf size: 38
DSolve[y''[x]+4*y'[x]==x+Exp[-4*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x^2}{8}-\frac {x}{16}-\frac {1}{16} e^{-4 x} (4 x+1+4 c_1)+c_2 \]