23.29 problem 660

Internal problem ID [3399]

Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section: Various 23
Problem number: 660.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]

Solve \begin {gather*} \boxed {x \left (x^{2}-6 y^{2}\right ) y^{\prime }-4 \left (x^{2}+3 y^{2}\right ) y=0} \end {gather*}

Solution by Maple

Time used: 0.155 (sec). Leaf size: 47

dsolve(x*(x^2-6*y(x)^2)*diff(y(x),x) = 4*(x^2+3*y(x)^2)*y(x),y(x), singsol=all)
 

\begin{align*} y \relax (x ) = -\frac {c_{1} \left (-1+\sqrt {-\frac {24 x^{6}}{c_{1}^{2}}+1}\right )}{12 x^{2}} \\ y \relax (x ) = \frac {c_{1} \left (1+\sqrt {-\frac {24 x^{6}}{c_{1}^{2}}+1}\right )}{12 x^{2}} \\ \end{align*}

Solution by Mathematica

Time used: 0.463 (sec). Leaf size: 67

DSolve[x(x^2-6 y[x]^2)y'[x]==4(x^2+3 y[x]^2)y[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {e^{c_1}-\sqrt {-24 x^6+e^{2 c_1}}}{12 x^2} \\ y(x)\to \frac {\sqrt {-24 x^6+e^{2 c_1}}+e^{c_1}}{12 x^2} \\ \end{align*}