44.5.78 problem 66 (b 3)

Internal problem ID [7140]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.2 Separable equations. Exercises 2.2 at page 53
Problem number : 66 (b 3)
Date solved : Sunday, March 30, 2025 at 11:48:37 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=-\frac {8 x +5}{3 y^{2}+1} \end{align*}

With initial conditions

\begin{align*} y \left (-1\right )&=4 \end{align*}

✓ Maple. Time used: 0.158 (sec). Leaf size: 80

ode:=diff(y(x),x) = -(5+8*x)/(3*y(x)^2+1); 
ic:=y(-1) = 4; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = \frac {\left (7236-432 x^{2}-540 x +12 \sqrt {1296 x^{4}+3240 x^{3}-41391 x^{2}-54270 x +363621}\right )^{{2}/{3}}-12}{6 \left (7236-432 x^{2}-540 x +12 \sqrt {1296 x^{4}+3240 x^{3}-41391 x^{2}-54270 x +363621}\right )^{{1}/{3}}} \]

✗ Mathematica

ode=D[y[x],x]== - (8*x+5)/(3*y[x]^2+1); 
ic={y[-1]==4}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Timed out

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((8*x + 5)/(3*y(x)**2 + 1) + Derivative(y(x), x),0) 
ics = {y(-1): 4} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out