76.4.14 problem 14

Internal problem ID [17329]
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 2.6 (Exact equations and integrating factors). Problems at page 100
Problem number : 14
Date solved : Thursday, March 13, 2025 at 09:27:31 AM
CAS classification : [_exact, _rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class A`]]

\begin{align*} 9 x^{2}+y-1-\left (4 y-x \right ) y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=0 \end{align*}

✓ Maple. Time used: 0.049 (sec). Leaf size: 25

ode:=9*x^2+y(x)-1-(4*y(x)-x)*diff(y(x),x) = 0; 
ic:=y(1) = 0; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = \frac {x}{4}-\frac {\sqrt {24 x^{3}+x^{2}-8 x -16}}{4} \]

✓ Mathematica. Time used: 0.15 (sec). Leaf size: 34

ode=(9*x^2+y[x]-1)-(4*y[x]-x)*D[y[x],x]==0; 
ic={y[1]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{4} \left (x+i \sqrt {-24 x^3-x^2+8 x+16}\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(9*x**2 - (-x + 4*y(x))*Derivative(y(x), x) + y(x) - 1,0) 
ics = {y(1): 0} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out