73.16.8 problem 24.1 (h)

Internal problem ID [15520]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 24. Variation of parameters. Additional exercises page 444
Problem number : 24.1 (h)
Date solved : Tuesday, January 28, 2025 at 08:00:58 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-9 y&=12 x^{3} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 29

dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)-9*y(x)=12*x^3,y(x), singsol=all)
 

\[ y = \frac {6 \ln \left (x \right ) x^{6}+\left (3 c_{1} -1\right ) x^{6}+3 c_{2}}{3 x^{3}} \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 29

DSolve[x^2*D[y[x],{x,2}]+x*D[y[x],x]-9*y[x]==12*x^3,y[x],x,IncludeSingularSolutions -> True]
 

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