49.16.4 problem 1(d)

Internal problem ID [7702]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 4. Linear equations with Regular Singular Points. Page 149
Problem number : 1(d)
Date solved : Monday, January 27, 2025 at 03:10:06 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y&=x^{2} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 18

dsolve(x^2*diff(y(x),x$2)-5*x*diff(y(x),x)+9*y(x)=x^2,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 22

DSolve[x^2*D[y[x],{x,2}]-5*x*D[y[x],x]+9*y[x]==x^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^2 (c_1 x+3 c_2 x \log (x)+1) \]