Internal problem ID [14096]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-\frac {\left (-4+x \right ) y^{3}}{x^{3} \left (y-2\right )}=0} \]
✓ Solution by Maple
Time used: 0.0 (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 \left (x \right ) &= -\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 \left (x \right ) &= \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: 0.66 (sec). Leaf size: 91
DSolve[y'[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*}