Internal problem ID [15339]
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: 570.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {y^{\prime \prime }+y^{\prime }=x^{2}-{\mathrm e}^{-x}+{\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 34
dsolve(diff(y(x),x$2)+diff(y(x),x)=x^2-exp(-x)+exp(x),y(x), singsol=all)
\[ y \left (x \right ) = \left (1+x -c_{1} \right ) {\mathrm e}^{-x}+\frac {x^{3}}{3}-x^{2}+2 x +c_{2} +\frac {{\mathrm e}^{x}}{2} \]
✓ Solution by Mathematica
Time used: 0.159 (sec). Leaf size: 43
DSolve[y''[x]+y'[x]==x^2-Exp[-x]+Exp[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x^3}{3}-x^2+2 x+\frac {e^x}{2}+e^{-x} (x+1-c_1)+c_2 \]