70.5.34 problem 35

Internal problem ID [18741]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.7 (Substitution Methods). Problems at page 108
Problem number : 35
Date solved : Thursday, October 02, 2025 at 03:30:18 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

\begin{align*} 4 x y y^{\prime }&=8 x^{2}+5 y^{2} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 35

ode:=4*x*y(x)*diff(y(x),x) = 8*x^2+5*y(x)^2; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \sqrt {x^{2} \left (-8+c_1 \sqrt {x}\right )} \\ y &= -\sqrt {x^{2} \left (-8+c_1 \sqrt {x}\right )} \\ \end{align*}

✓ Mathematica. Time used: 3.577 (sec). Leaf size: 47

ode=4*x*y[x]*D[y[x],x]==8*x^2+5*y[x]^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\sqrt {x^2 \left (-8+c_1 \sqrt {x}\right )}\\ y(x)&\to \sqrt {x^2 \left (-8+c_1 \sqrt {x}\right )} \end{align*}

✓ Sympy. Time used: 0.265 (sec). Leaf size: 36

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-8*x**2 + 4*x*y(x)*Derivative(y(x), x) - 5*y(x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - \sqrt {C_{1} x^{\frac {5}{2}} - 8 x^{2}}, \ y{\left (x \right )} = \sqrt {C_{1} x^{\frac {5}{2}} - 8 x^{2}}\right ] \]