Internal problem ID [4834]
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]]
\[ \boxed {y^{\prime \prime }-5 y^{\prime }+6 y=2 \,{\mathrm e}^{x}+6 x -5} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = c_{2} {\mathrm e}^{2 x}+c_{1} {\mathrm e}^{3 x}+x +{\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.191 (sec). Leaf size: 26
DSolve[y''[x]-5*y'[x]+6*y[x]==2*Exp[x]+6*x-5,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x+e^x+c_1 e^{2 x}+c_2 e^{3 x} \]