73.4.17 problem 5.2 (g)

Internal problem ID [15028]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 5. LINEAR FIRST ORDER EQUATIONS. Additional exercises. page 103
Problem number : 5.2 (g)
Date solved : Monday, March 31, 2025 at 01:13:16 PM
CAS classification : [_linear]

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

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

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

\[ y = -\frac {2 \sqrt {x}}{5}+c_1 \,x^{3} \]

✓ Mathematica. Time used: 0.028 (sec). Leaf size: 21

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

\[ y(x)\to -\frac {2 \sqrt {x}}{5}+c_1 x^3 \]

✓ Sympy. Time used: 0.255 (sec). Leaf size: 15

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

\[ y{\left (x \right )} = C_{1} x^{3} - \frac {2 \sqrt {x}}{5} \]