73.9.28 problem 14.3 (d)

Internal problem ID [15289]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 14. Higher order equations and the reduction of order method. Additional exercises page 277
Problem number : 14.3 (d)
Date solved : Tuesday, January 28, 2025 at 07:51:37 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-20 y&=27 x^{5} \end{align*}

Using reduction of order method given that one solution is

\begin{align*} y&=x^{5} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 29

dsolve([x^2*diff(y(x),x$2)-20*y(x)=27*x^5,x^5],singsol=all)
 

\[ y = \frac {9 \ln \left (x \right ) x^{9}+\left (3 c_{2} -1\right ) x^{9}+3 c_{1}}{3 x^{4}} \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 29

DSolve[x^2*D[y[x],{x,2}]-20*y[x]==27*x^5,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 3 x^5 \log (x)+\left (-\frac {1}{3}+c_2\right ) x^5+\frac {c_1}{x^4} \]