35.8.16 problem 16

Internal problem ID [6223]
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
Date solved : Monday, January 27, 2025 at 01:48:38 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&={\mathrm e}^{2 x} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 21

dsolve(diff(y(x),x$2)-5*diff(y(x),x)+6*y(x)=exp(2*x),y(x), singsol=all)
 

\[ y = \left (-x +c_{1} \right ) {\mathrm e}^{2 x}+c_{2} {\mathrm e}^{3 x} \]

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 24

DSolve[D[y[x],{x,2}]-5*D[y[x],x]+6*y[x]==Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{2 x} \left (-x+c_2 e^x-1+c_1\right ) \]