75.17.20 problem 570

Internal problem ID [17069]
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 : 570
Date solved : Tuesday, January 28, 2025 at 09:49:12 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} y^{\prime \prime }+y^{\prime }&=x^{2}-{\mathrm e}^{-x}+{\mathrm e}^{x} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 34

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

\[ y = \left (1+x -c_{1} \right ) {\mathrm e}^{-x}+\frac {x^{3}}{3}-x^{2}+2 x +c_{2} +\frac {{\mathrm e}^{x}}{2} \]

✓ Solution by Mathematica

Time used: 4.994 (sec). Leaf size: 50

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

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