6.10 problem 10

Internal problem ID [4308]

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.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]

Solve \begin {gather*} \boxed {y^{\prime \prime }-6 y^{\prime }+9 y-6 \,{\mathrm e}^{3 x}=0} \end {gather*}

Solution by Maple

Time used: 0.015 (sec). Leaf size: 27

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

\[ y \relax (x ) = c_{2} {\mathrm e}^{3 x}+c_{1} x \,{\mathrm e}^{3 x}+3 \,{\mathrm e}^{3 x} x^{2} \]

Solution by Mathematica

Time used: 0.01 (sec). Leaf size: 22

DSolve[y''[x]-6*y'[x]+9*y[x]==6*Exp[3*x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to e^{3 x} (x (3 x+c_2)+c_1) \\ \end{align*}