89.7.26 problem 25

Internal problem ID [24457]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 4. Additional topics on equations of first order and first degree. Exercises at page 61
Problem number : 25
Date solved : Thursday, October 02, 2025 at 10:38:03 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} 2 x y y^{\prime }&=y^{2}-2 x^{3} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=2 \\ \end{align*}

✓ Maple. Time used: 0.052 (sec). Leaf size: 14

ode:=2*x*y(x)*diff(y(x),x) = y(x)^2-2*x^3; 
ic:=[y(1) = 2]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \sqrt {-x \left (x^{2}-5\right )} \]

✓ Mathematica. Time used: 0.214 (sec). Leaf size: 17

ode=2*x*y[x]*D[y[x],x]==y[x]^2-2*x^3; 
ic={y[1]==2}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \sqrt {-x \left (x^2-5\right )} \end{align*}

✓ Sympy. Time used: 0.291 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x**3 + 2*x*y(x)*Derivative(y(x), x) - y(x)**2,0) 
ics = {y(1): 2} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \sqrt {x \left (5 - x^{2}\right )} \]