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 : Tuesday, February 04, 2025 at 12:36:21 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*}

✓ Solution by Maple

Time used: 0.067 (sec). Leaf size: 80

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

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

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

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

Timed out