38.1.37 problem 39

Internal problem ID [8198]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Exercises 1.1 at page 12
Problem number : 39
Date solved : Tuesday, September 30, 2025 at 05:18:40 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y&=0 \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);
 

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

✓ Mathematica. Time used: 0.077 (sec). Leaf size: 133

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

\begin{align*} y(x)&\to 7^{-\frac {1}{2} i \left (\sqrt {59}-i\right )} x^{\frac {1}{2}-\frac {i \sqrt {59}}{2}} \left (c_2 x^{i \sqrt {59}} \operatorname {Hypergeometric1F1}\left (-\frac {1}{2}-\frac {i \sqrt {59}}{2},1-i \sqrt {59},-\frac {7}{x}\right )+7^{i \sqrt {59}} c_1 \operatorname {Hypergeometric1F1}\left (\frac {1}{2} i \left (i+\sqrt {59}\right ),1+i \sqrt {59},-\frac {7}{x}\right )\right ) \end{align*}

✓ Sympy. Time used: 0.091 (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)
 

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