44.5.10 problem 10

Internal problem ID [7072]
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 : 10
Date solved : Monday, January 27, 2025 at 02:46:54 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {\left (2 y+3\right )^{2}}{\left (4 x +5\right )^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 28

dsolve(diff(y(x),x)=( (2*y(x)+3)/(4*x+5))^2,y(x), singsol=all)
 

\[ y = \frac {\left (-48 x -60\right ) c_{1} -8 x -7}{-2+\left (32 x +40\right ) c_{1}} \]

✓ Solution by Mathematica

Time used: 0.285 (sec). Leaf size: 42

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

\begin{align*} y(x)\to -\frac {8 (1+6 c_1) x+7+60 c_1}{-2+8 c_1 (4 x+5)} \\ y(x)\to -\frac {3}{2} \\ \end{align*}