35.6.10 problem 10

Internal problem ID [6160]
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 : 10
Date solved : Monday, January 27, 2025 at 01:38:45 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 19

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

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

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 23

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

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