Internal problem ID [4326]
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: 34.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-5 y^{\prime }+6 y-2 \,{\mathrm e}^{x}-6 x +5=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 20
dsolve(diff(y(x),x$2)-5*diff(y(x),x)+6*y(x)=2*exp(x)+6*x-5,y(x), singsol=all)
\[ y \relax (x ) = c_{2} {\mathrm e}^{2 x}+c_{1} {\mathrm e}^{3 x}+{\mathrm e}^{x}+x \]
✓ Solution by Mathematica
Time used: 0.063 (sec). Leaf size: 26
DSolve[y''[x]-5*y'[x]+6*y[x]==2*Exp[x]+6*x-5,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x+e^x+c_1 e^{2 x}+c_2 e^{3 x} \\ \end{align*}