Internal problem ID [4371]
Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley.
2006
Section: Chapter 8, Ordinary differential equations. Section 13. Miscellaneous problems. page
466
Problem number: 16.
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-{\mathrm e}^{2 x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 24
dsolve(diff(y(x),x$2)-5*diff(y(x),x)+6*y(x)=exp(2*x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} {\mathrm e}^{2 x}+c_{1} {\mathrm e}^{3 x}-x \,{\mathrm e}^{2 x} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 24
DSolve[y''[x]-5*y'[x]+6*y[x]==Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{2 x} \left (-x+c_2 e^x-1+c_1\right ) \\ \end{align*}