67.4.20 problem 5.2 (j)

Internal problem ID [16389]
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 (j)
Date solved : Thursday, October 02, 2025 at 01:27:28 PM
CAS classification : [_linear]

\begin{align*} 2 \sqrt {x}\, y^{\prime }+y&=2 x \,{\mathrm e}^{-\sqrt {x}} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 21

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

\[ y = \frac {\left (2 x^{{3}/{2}}+3 c_1 \right ) {\mathrm e}^{-\sqrt {x}}}{3} \]

✓ Mathematica. Time used: 0.072 (sec). Leaf size: 30

ode=2*Sqrt[x]*D[y[x],x]+y[x]==2*x*Exp[-Sqrt[x]]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{3} e^{-\sqrt {x}} \left (2 x^{3/2}+3 c_1\right ) \end{align*}

✓ Sympy. Time used: 0.384 (sec). Leaf size: 19

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

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