35.6.24 problem 24

Internal problem ID [6174]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 6. SECOND-ORDER LINEAR EQUATIONSWITH CONSTANT COEFFICIENTS AND RIGHT-HAND SIDE NOT ZERO. page 422
Problem number : 24
Date solved : Monday, January 27, 2025 at 01:46:32 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=12 x \,{\mathrm e}^{3 x} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 19

dsolve(diff(y(x),x$2)-6*diff(y(x),x)+9*y(x)=12*x*exp(3*x),y(x), singsol=all)
 

\[ y = {\mathrm e}^{3 x} \left (2 x^{3}+c_1 x +c_2 \right ) \]

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 23

DSolve[D[y[x],{x,2}]-6D[y[x],x]+9*y[x]==12*x*Exp[3*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{3 x} \left (2 x^3+c_2 x+c_1\right ) \]