73.7.5 problem 5

Internal problem ID [15092]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 8. Review exercises for part of part II. page 143
Problem number : 5
Date solved : Monday, March 31, 2025 at 01:23:27 PM
CAS classification : [_quadrature]

\begin{align*} x^{2} y^{\prime }-\sqrt {x}&=3 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 16

ode:=x^2*diff(y(x),x)-x^(1/2) = 3; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {3}{x}-\frac {2}{\sqrt {x}}+c_1 \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 20

ode=x^2*D[y[x],x]-Sqrt[x]==3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -\frac {2}{\sqrt {x}}-\frac {3}{x}+c_1 \]

✓ Sympy. Time used: 0.202 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-sqrt(x) + x**2*Derivative(y(x), x) - 3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} - \frac {3}{x} - \frac {2}{\sqrt {x}} \]