50.12.8 problem 6(b)

Internal problem ID [8012]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 2. Second-Order Linear Equations. Section 2.4. THE USE OF A KNOWN SOLUTION TO FIND ANOTHER. Page 74
Problem number : 6(b)
Date solved : Monday, January 27, 2025 at 03:36:47 PM
CAS classification : [[_Emden, _Fowler]]

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

Using reduction of order method given that one solution is

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 15

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

\[ y = \frac {c_{2} x^{3}+c_{1}}{x^{2}} \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 16

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

\[ y(x)\to \frac {c_1}{x^2}+c_2 x \]