8.6.20 problem 20

Internal problem ID [790]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Chapter 1 review problems. Page 78
Problem number : 20
Date solved : Tuesday, March 04, 2025 at 11:48:44 AM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.000 (sec). Leaf size: 15

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

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

✓ Mathematica. Time used: 0.035 (sec). Leaf size: 19

ode=3*y[x]+x*D[y[x],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: 0.187 (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)
 

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