49.13.1 problem 1(a)

Internal problem ID [7677]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 3. Linear equations with variable coefficients. Page 121
Problem number : 1(a)
Date solved : Monday, January 27, 2025 at 03:09:43 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{2} y^{\prime \prime }-7 x y^{\prime }+15 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: 0.003 (sec). Leaf size: 15

dsolve([x^2*diff(y(x),x$2)-7*x*diff(y(x),x)+15*y(x)=0,x^3],singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 18

DSolve[x^2*D[y[x],{x,2}]-7*x*D[y[x],x]+15*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^3 \left (c_2 x^2+c_1\right ) \]