Internal problem ID [15295]
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: 525.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+5 y^{\prime }+6 y=10 \left (1-x \right ) {\mathrm e}^{-2 x}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 26
dsolve(diff(y(x),x$2)+5*diff(y(x),x)+6*y(x)=10*(1-x)*exp(-2*x),y(x), singsol=all)
\[ y \left (x \right ) = \left (-5 x^{2}+c_{1} +20 x \right ) {\mathrm e}^{-2 x}+{\mathrm e}^{-3 x} c_{2} \]
✓ Solution by Mathematica
Time used: 0.06 (sec). Leaf size: 30
DSolve[y''[x]+5*y'[x]+6*y[x]==10*(1-x)*Exp[-2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-3 x} \left (e^x \left (-5 x^2+20 x-20+c_2\right )+c_1\right ) \]