Internal problem ID [15294]
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: 524.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {y^{\prime \prime }+3 y^{\prime }=3 x \,{\mathrm e}^{-3 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 25
dsolve(diff(y(x),x$2)+3*diff(y(x),x)=3*x*exp(-3*x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (-9 x^{2}-6 c_{1} -6 x -2\right ) {\mathrm e}^{-3 x}}{18}+c_{2} \]
✓ Solution by Mathematica
Time used: 0.088 (sec). Leaf size: 31
DSolve[y''[x]+3*y'[x]==3*x*Exp[-3*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_2-\frac {1}{18} e^{-3 x} \left (9 x^2+6 x+2+6 c_1\right ) \]