35.3.4 problem 4

Internal problem ID [6108]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 3. Linear First-Order Equations. page 403
Problem number : 4
Date solved : Sunday, March 30, 2025 at 10:39:00 AM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 16

ode:=2*x*diff(y(x),x)+y(x) = 2*x^(5/2); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.038 (sec). Leaf size: 22

ode=2*x*D[y[x],x]+y[x]==2*x^(5/2); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.205 (sec). Leaf size: 14

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

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