89.10.20 problem 20

Internal problem ID [24513]
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 77
Problem number : 20
Date solved : Thursday, October 02, 2025 at 10:44:15 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, _Bernoulli]

\begin{align*} 4 y+3 \left (2 x -1\right ) \left (y^{\prime }+y^{4}\right )&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 1.295 (sec). Leaf size: 16

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

\[ y = \frac {1}{\left (10 x^{2}-13 x +4\right )^{{1}/{3}}} \]

✓ Mathematica. Time used: 0.648 (sec). Leaf size: 19

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

\begin{align*} y(x)&\to \frac {1}{\sqrt [3]{10 x^2-13 x+4}} \end{align*}

✓ Sympy. Time used: 4.511 (sec). Leaf size: 34

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((6*x - 3)*(y(x)**4 + Derivative(y(x), x)) + 4*y(x),0) 
ics = {y(1): 1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {\sqrt [3]{2} \cdot 3^{\frac {2}{3}} \sqrt [3]{\frac {1}{\frac {20 x^{2}}{3} - \frac {26 x}{3} + \frac {8}{3}}}}{3} \]