Internal problem ID [3837]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 21
Problem number: 587.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _dAlembert]
\[ \boxed {8 y y^{\prime } x^{3}-6 x^{2} y^{2}-y^{4}=-3 x^{4}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 54
dsolve(8*x^3*y(x)*diff(y(x),x)+3*x^4-6*x^2*y(x)^2-y(x)^4 = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {x \sqrt {-\left (c_{1} x -1\right ) \left (c_{1} x +3\right )}}{c_{1} x -1} y \left (x \right ) = -\frac {x \sqrt {-\left (c_{1} x -1\right ) \left (c_{1} x +3\right )}}{c_{1} x -1} \end{align*}
✓ Solution by Mathematica
Time used: 5.038 (sec). Leaf size: 160
DSolve[8 x^3 y[x] y'[x]+3 x^4 -6 x^2 y[x]^2 -y[x]^4==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {-x^2 \left (3+e^{8 c_1} x\right )}}{\sqrt {-1+e^{8 c_1} x}} y(x)\to \frac {\sqrt {-x^2 \left (3+e^{8 c_1} x\right )}}{\sqrt {-1+e^{8 c_1} x}} y(x)\to -i \sqrt {3} \sqrt {-x^2} y(x)\to i \sqrt {3} \sqrt {-x^2} y(x)\to \frac {x^{5/2}}{\sqrt {-x^3}} y(x)\to \frac {\sqrt {-x^3}}{\sqrt {x}} \end{align*}