75.17.2 problem 552

Internal problem ID [17051]
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. Superposition principle. Exercises page 137
Problem number : 552
Date solved : Tuesday, January 28, 2025 at 09:47:42 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} y^{\prime \prime }+4 y^{\prime }&=x +{\mathrm e}^{-4 x} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 28

dsolve(diff(y(x),x$2)+4*diff(y(x),x)=x+exp(-4*x),y(x), singsol=all)
 

\[ y = \frac {\left (-4 x -4 c_{1} -1\right ) {\mathrm e}^{-4 x}}{16}+\frac {x^{2}}{8}-\frac {x}{16}+c_{2} \]

✓ Solution by Mathematica

Time used: 5.549 (sec). Leaf size: 44

DSolve[D[y[x],{x,2}]+4*D[y[x],x]==x+Exp[-4*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \int _1^xe^{-4 K[2]} \left (c_1+\int _1^{K[2]}\left (e^{4 K[1]} K[1]+1\right )dK[1]\right )dK[2]+c_2 \]