74.1.52 problem 72

Internal problem ID [15832]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 1. Introduction to Differential Equations. Exercises 1.1, page 10
Problem number : 72
Date solved : Tuesday, January 28, 2025 at 08:08:29 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 76

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

\begin{align*} y &= -\frac {\left (x +\sqrt {8+\left (4 c_{1} +1\right ) x^{2}-4 x}\right ) x}{2 c_{1} x^{2}-2 x +4} \\ y &= \frac {x \left (-x +\sqrt {8+\left (4 c_{1} +1\right ) x^{2}-4 x}\right )}{2 c_{1} x^{2}-2 x +4} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.916 (sec). Leaf size: 91

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

\begin{align*} y(x)\to \frac {x \left (-x+\sqrt {x^2+4 c_1 x^2-4 x+8}\right )}{2 c_1 x^2-2 x+4} \\ y(x)\to -\frac {x \left (x+\sqrt {x^2+4 c_1 x^2-4 x+8}\right )}{2 c_1 x^2-2 x+4} \\ y(x)\to 0 \\ \end{align*}