9.1.1 problem problem 38

Internal problem ID [928]
Book : Differential equations and linear algebra, 4th ed., Edwards and Penney
Section : Section 5.2, Higher-Order Linear Differential Equations. General solutions of Linear Equations. Page 288
Problem number : problem 38
Date solved : Monday, January 27, 2025 at 03:22:35 AM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-9 y&=0 \end{align*}

Using reduction of order method given that one solution is

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 15

dsolve([x^2*diff(y(x),x$2)+x*diff(y(x),x)-9*y(x)=0,x^3],singsol=all)
 

\[ y = \frac {c_2 \,x^{6}+c_1}{x^{3}} \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 18

DSolve[x^2*D[y[x],{x,2}]+x*D[y[x],x]-9*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_2 x^6+c_1}{x^3} \]