7.7.20 problem 20

Internal problem ID [198]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Review problems at page 98
Problem number : 20
Date solved : Saturday, March 29, 2025 at 04:44:20 PM
CAS classification : [_linear]

\begin{align*} x y^{\prime }+3 y&=\frac {3}{x^{{3}/{2}}} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 15

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

\[ y = \frac {2 x^{{3}/{2}}+c_1}{x^{3}} \]

✓ Mathematica. Time used: 0.036 (sec). Leaf size: 19

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

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

✓ Sympy. Time used: 0.183 (sec). Leaf size: 14

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

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