40.9.6 problem 16

Internal problem ID [6716]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 14. Linear equations with constant coefficients. Supplemetary problems. Page 92
Problem number : 16
Date solved : Monday, January 27, 2025 at 02:24:41 PM
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: 0.003 (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)
 

\[ y = \left (c_1 x +c_2 \right ) {\mathrm e}^{3 x}+{\mathrm e}^{2 x} \]

✓ Solution by Mathematica

Time used: 0.026 (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]
 

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