29.21.11 problem 587

Internal problem ID [5181]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 21
Problem number : 587
Date solved : Monday, January 27, 2025 at 10:18:08 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} 8 x^{3} y y^{\prime }+3 x^{4}-6 x^{2} y^{2}-y^{4}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.018 (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: 5.406 (sec). Leaf size: 160

DSolve[8 x^3 y[x] D[y[x],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*}