Internal problem ID [4322]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-6 y^{\prime }+9 y-12 x \,{\mathrm e}^{3 x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 27
dsolve(diff(y(x),x$2)-6*diff(y(x),x)+9*y(x)=12*x*exp(3*x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} {\mathrm e}^{3 x}+c_{1} x \,{\mathrm e}^{3 x}+2 x^{3} {\mathrm e}^{3 x} \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 23
DSolve[y''[x]-6y'[x]+9*y[x]==12*x*Exp[3*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{3 x} \left (2 x^3+c_2 x+c_1\right ) \\ \end{align*}