4.5.14 problem 14

Internal problem ID [1206]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.6. Page 100
Problem number : 14
Date solved : Tuesday, September 30, 2025 at 04:29:25 AM
CAS classification : [_exact, _rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class A`]]

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

With initial conditions

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

✓ Maple. Time used: 0.077 (sec). Leaf size: 25

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

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

✓ Mathematica. Time used: 0.093 (sec). Leaf size: 34

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

\begin{align*} y(x)&\to \frac {1}{4} \left (x+i \sqrt {-24 x^3-x^2+8 x+16}\right ) \end{align*}

✗ 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