75.16.51 problem 524

Internal problem ID [17024]
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. Trial and error method. Exercises page 132
Problem number : 524
Date solved : Tuesday, January 28, 2025 at 09:45:48 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} y^{\prime \prime }+3 y^{\prime }&=3 x \,{\mathrm e}^{-3 x} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 25

dsolve(diff(y(x),x$2)+3*diff(y(x),x)=3*x*exp(-3*x),y(x), singsol=all)
 

\[ y = \frac {\left (-9 x^{2}-6 c_{1} -6 x -2\right ) {\mathrm e}^{-3 x}}{18}+c_{2} \]

✓ Solution by Mathematica

Time used: 2.529 (sec). Leaf size: 69

DSolve[D[y[x],{x,2}]+3*D[y[x],x]==3*x*Exp[-3*x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \int _1^x\frac {1}{2} e^{-3 K[1]} \left (3 K[1]^2+2 c_1\right )dK[1]+c_2 \\ y(x)\to -\frac {1}{18} e^{-3 x} \left (9 x^2+6 x+2\right )+\frac {17}{18 e^3}+c_2 \\ \end{align*}