20.11.10 problem Problem 13

Internal problem ID [3792]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 8, Linear differential equations of order n. Section 8.9, Reduction of Order. page 572
Problem number : Problem 13
Date solved : Monday, January 27, 2025 at 08:02:22 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=15 \,{\mathrm e}^{3 x} \sqrt {x} \end{align*}

Using reduction of order method given that one solution is

\begin{align*} y&={\mathrm e}^{3 x} \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 19

dsolve([diff(y(x),x$2)-6*diff(y(x),x)+9*y(x)=15*exp(3*x)*sqrt(x),exp(3*x)],singsol=all)
 

\[ y \left (x \right ) = {\mathrm e}^{3 x} \left (c_{2} +c_{1} x +4 x^{{5}/{2}}\right ) \]

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 25

DSolve[D[y[x],{x,2}]-6*D[y[x],x]+9*y[x]==15*Exp[3*x]*Sqrt[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{3 x} \left (4 x^{5/2}+c_2 x+c_1\right ) \]