Internal problem ID [10151]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter 2, differential equations of the first order and the first degree. Article 17. Other forms
which Integrating factors can be found. Page 25
Problem number: Ex 4.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {x^{3} y-y^{4}+\left (x y^{3}-x^{4}\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 37
dsolve((x^3*y(x)-y(x)^4)+(y(x)^3*x-x^4)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \left (-\frac {1}{2}-\frac {i \sqrt {3}}{2}\right ) x \\ y \relax (x ) = \left (-\frac {1}{2}+\frac {i \sqrt {3}}{2}\right ) x \\ y \relax (x ) = x \\ y \relax (x ) = x c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.031 (sec). Leaf size: 99
DSolve[(x^3*y[x]-y[x]^4)+(y[x]^3*x-x^4)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \\ y(x)\to -\frac {1}{2} i \left (\sqrt {3}-i\right ) x \\ y(x)\to \frac {1}{2} i \left (\sqrt {3}+i\right ) x \\ y(x)\to c_1 x \\ y(x)\to x \\ y(x)\to -\frac {1}{2} i \left (\sqrt {3}-i\right ) x \\ y(x)\to \frac {1}{2} i \left (\sqrt {3}+i\right ) x \\ \end{align*}