29.24.19 problem 681

Internal problem ID [5272]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 24
Problem number : 681
Date solved : Monday, January 27, 2025 at 10:54:30 AM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, _dAlembert]

\begin{align*} \left (3 x^{2}+y^{2}\right ) y y^{\prime }+x \left (x^{2}+3 y^{2}\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.119 (sec). Leaf size: 119

dsolve((3*x^2+y(x)^2)*y(x)*diff(y(x),x)+x*(x^2+3*y(x)^2) = 0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= \frac {\sqrt {-3 c_{1} x^{2}-\sqrt {8 c_{1}^{2} x^{4}+1}}}{\sqrt {c_{1}}} \\ y \left (x \right ) &= \frac {\sqrt {-3 c_{1} x^{2}+\sqrt {8 c_{1}^{2} x^{4}+1}}}{\sqrt {c_{1}}} \\ y \left (x \right ) &= -\frac {\sqrt {-3 c_{1} x^{2}-\sqrt {8 c_{1}^{2} x^{4}+1}}}{\sqrt {c_{1}}} \\ y \left (x \right ) &= -\frac {\sqrt {-3 c_{1} x^{2}+\sqrt {8 c_{1}^{2} x^{4}+1}}}{\sqrt {c_{1}}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 8.414 (sec). Leaf size: 245

DSolve[(3*x^2+y[x]^2)*y[x]*D[y[x],x]+x*(x^2+3*y[x]^2)==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\sqrt {-3 x^2-\sqrt {8 x^4+e^{4 c_1}}} \\ y(x)\to \sqrt {-3 x^2-\sqrt {8 x^4+e^{4 c_1}}} \\ y(x)\to -\sqrt {-3 x^2+\sqrt {8 x^4+e^{4 c_1}}} \\ y(x)\to \sqrt {-3 x^2+\sqrt {8 x^4+e^{4 c_1}}} \\ y(x)\to -\sqrt {-2 \sqrt {2} \sqrt {x^4}-3 x^2} \\ y(x)\to \sqrt {-2 \sqrt {2} \sqrt {x^4}-3 x^2} \\ y(x)\to -\sqrt {2 \sqrt {2} \sqrt {x^4}-3 x^2} \\ y(x)\to \sqrt {2 \sqrt {2} \sqrt {x^4}-3 x^2} \\ \end{align*}