Internal problem ID [11683]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]
\[ \boxed {y^{\prime }-\frac {4 y^{2} x^{3}-3 x^{2} y}{x^{3}-2 y x^{4}}=0} \]
✓ Solution by Maple
Time used: 0.078 (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 \left (x \right ) &= \frac {x -\sqrt {x^{2}+4 c_{1}}}{2 x^{2}} \\ y \left (x \right ) &= \frac {x +\sqrt {x^{2}+4 c_{1}}}{2 x^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.575 (sec). Leaf size: 78
DSolve[y'[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*}