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 : Sunday, March 30, 2025 at 12:18:46 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*}

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

ode:=x^2*diff(diff(y(x),x),x)-7*x*diff(y(x),x)+15*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = x^{3} \left (c_2 \,x^{2}+c_1 \right ) \]

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

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

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

✓ Sympy. Time used: 0.175 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) - 7*x*Derivative(y(x), x) + 15*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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