23.2.15 problem 6(d)

Internal problem ID [4132]
Book : Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section : Chapter 3. Linear differential equations of second order. Exercises at page 31
Problem number : 6(d)
Date solved : Monday, January 27, 2025 at 08:37:09 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{2 x} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 19

dsolve(diff(y(x),x$2)-6*diff(y(x),x)+9*y(x)=exp(2*x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 24

DSolve[D[y[x],{x,2}]-6*D[y[x],x]+9*y[x]==Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
 

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