29.23.29 problem 660

Internal problem ID [5251]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 23
Problem number : 660
Date solved : Monday, January 27, 2025 at 10:49:22 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} x \left (x^{2}-6 y^{2}\right ) y^{\prime }&=4 \left (x^{2}+3 y^{2}\right ) y \end{align*}

✓ Solution by Maple

Time used: 1.006 (sec). Leaf size: 53

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

✓ Solution by Mathematica

Time used: 1.318 (sec). Leaf size: 67

DSolve[x(x^2-6 y[x]^2)D[y[x],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*}