64.6.9 problem 9

Internal problem ID [13359]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, Miscellaneous Review. Exercises page 60
Problem number : 9
Date solved : Tuesday, January 28, 2025 at 05:31:54 AM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.186 (sec). Leaf size: 41

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

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

✓ Solution by Mathematica

Time used: 0.760 (sec). Leaf size: 78

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

\begin{align*} y(x)\to \frac {x^3-\sqrt {x^2} \sqrt {x^4+4 c_1 x^2}}{2 x^4} \\ y(x)\to \frac {x^3+\sqrt {x^2} \sqrt {x^4+4 c_1 x^2}}{2 x^4} \\ \end{align*}