62.10.4 problem Ex 4

Internal problem ID [12841]
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
Date solved : Tuesday, January 28, 2025 at 04:26:32 AM
CAS classification : [_separable]

\begin{align*} x^{3} y-y^{4}+\left (x y^{3}-x^{4}\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (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 &= -\frac {\left (1+i \sqrt {3}\right ) x}{2} \\ y &= \frac {\left (i \sqrt {3}-1\right ) x}{2} \\ y &= x \\ y &= c_{1} x \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 99

DSolve[(x^3*y[x]-y[x]^4)+(y[x]^3*x-x^4)*D[y[x],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*}