89.7.27 problem 26

Internal problem ID [24458]
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 : 26
Date solved : Thursday, October 02, 2025 at 10:38:05 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} y^{4}-2 y x +3 x^{2} y^{\prime }&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.047 (sec). Leaf size: 21

ode:=y(x)^4-2*x*y(x)+3*x^2*diff(y(x),x) = 0; 
ic:=[y(2) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {\left (x^{2} \left (x +2\right )^{2}\right )^{{1}/{3}}}{x +2} \]

✓ Mathematica. Time used: 0.124 (sec). Leaf size: 18

ode=(y[x]^4-2*x*y[x])+(3*x^2)*D[y[x],x]==0; 
ic={y[2]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {x^{2/3}}{\sqrt [3]{x+2}} \end{align*}

✓ Sympy. Time used: 1.028 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*x**2*Derivative(y(x), x) - 2*x*y(x) + y(x)**4,0) 
ics = {y(2): 1} 
dsolve(ode,func=y(x),ics=ics)
 

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