68.18.53 problem 59

Internal problem ID [17897]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number : 59
Date solved : Thursday, October 02, 2025 at 02:29:22 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} 2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=1 \\ y^{\prime }\left (1\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.053 (sec). Leaf size: 15

ode:=2*x^2*diff(diff(y(x),x),x)+5*x*diff(y(x),x)+y(x) = 0; 
ic:=[y(1) = 1, D(y)(1) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {2}{\sqrt {x}}-\frac {1}{x} \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 18

ode=2*x^2*D[y[x],{x,2}]+5*x*D[y[x],x]+y[x]==0; 
ic={y[1]==1,Derivative[1][y][1]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {2 \sqrt {x}-1}{x} \end{align*}

✓ Sympy. Time used: 0.106 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x**2*Derivative(y(x), (x, 2)) + 5*x*Derivative(y(x), x) + y(x),0) 
ics = {y(1): 1, Subs(Derivative(y(x), x), x, 1): 0} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = - \frac {1}{x} + \frac {2}{\sqrt {x}} \]