7.4.7 problem 7

Internal problem ID [79]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.5 (linear equations). Problems at page 54
Problem number : 7
Date solved : Saturday, March 29, 2025 at 04:30:24 PM
CAS classification : [_linear]

\begin{align*} 2 x y^{\prime }+y&=10 \sqrt {x} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 13

ode:=2*x*diff(y(x),x)+y(x) = 10*x^(1/2); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {5 x +c_1}{\sqrt {x}} \]

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 17

ode=2*x*D[y[x],x]+y[x]==10*Sqrt[x]; 
DSolve[ode,y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {5 x+c_1}{\sqrt {x}} \]

✓ Sympy. Time used: 0.189 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-10*sqrt(x) + 2*x*Derivative(y(x), x) + y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} + 5 x}{\sqrt {x}} \]