87.4.17 problem 28

Internal problem ID [23283]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 1. Elementary methods. First order differential equations. Exercise at page 37
Problem number : 28
Date solved : Thursday, October 02, 2025 at 09:28:30 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }-2 y x&=4 x \sqrt {y} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 18

ode:=diff(y(x),x)-2*x*y(x) = 4*x*y(x)^(1/2); 
dsolve(ode,y(x), singsol=all);
 

\[ 2-{\mathrm e}^{\frac {x^{2}}{2}} c_1 +\sqrt {y} = 0 \]

✓ Mathematica. Time used: 0.13 (sec). Leaf size: 31

ode=D[y[x],x]-2*x*y[x]==4*x*y[x]^(1/2); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \left (-2+e^{\frac {1}{2} \left (x^2+c_1\right )}\right ){}^2\\ y(x)&\to 0\\ y(x)&\to 4 \end{align*}

✓ Sympy. Time used: 0.324 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-4*x*sqrt(y(x)) - 2*x*y(x) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = - 4 e^{\frac {C_{1}}{2} + \frac {x^{2}}{2}} + e^{C_{1} + x^{2}} + 4 \]