15.13.1 problem 1

Internal problem ID [3170]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 22, page 99
Problem number : 1
Date solved : Monday, January 27, 2025 at 07:24:52 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{3 x} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 19

dsolve(diff(y(x),x$2)-6*diff(y(x),x)+9*y(x)=exp(3*x),y(x), singsol=all)
 

\[ y = {\mathrm e}^{3 x} \left (c_2 +c_{1} x +\frac {1}{2} x^{2}\right ) \]

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 27

DSolve[D[y[x],{x,2}]-6*D[y[x],x]+9*y[x]==Exp[3*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} e^{3 x} \left (x^2+2 c_2 x+2 c_1\right ) \]