29.24.24 problem 686

Internal problem ID [5277]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 24
Problem number : 686
Date solved : Monday, January 27, 2025 at 10:57:26 AM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, _dAlembert]

\begin{align*} \left (5 x^{2}+2 y^{2}\right ) y y^{\prime }+x \left (x^{2}+5 y^{2}\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.123 (sec). Leaf size: 125

dsolve((5*x^2+2*y(x)^2)*y(x)*diff(y(x),x)+x*(x^2+5*y(x)^2) = 0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= -\frac {\sqrt {-10 c_{1} x^{2}-2 \sqrt {23 c_{1}^{2} x^{4}+2}}}{2 \sqrt {c_{1}}} \\ y \left (x \right ) &= \frac {\sqrt {-10 c_{1} x^{2}-2 \sqrt {23 c_{1}^{2} x^{4}+2}}}{2 \sqrt {c_{1}}} \\ y \left (x \right ) &= -\frac {\sqrt {-10 c_{1} x^{2}+2 \sqrt {23 c_{1}^{2} x^{4}+2}}}{2 \sqrt {c_{1}}} \\ y \left (x \right ) &= \frac {\sqrt {-10 c_{1} x^{2}+2 \sqrt {23 c_{1}^{2} x^{4}+2}}}{2 \sqrt {c_{1}}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 23.791 (sec). Leaf size: 295

DSolve[(5*x^2+2*y[x]^2)*y[x]*D[y[x],x]+x*(x^2+5*y[x]^2)==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {\sqrt {-5 x^2-\sqrt {23 x^4+2 e^{4 c_1}}}}{\sqrt {2}} \\ y(x)\to \frac {\sqrt {-5 x^2-\sqrt {23 x^4+2 e^{4 c_1}}}}{\sqrt {2}} \\ y(x)\to -\frac {\sqrt {-5 x^2+\sqrt {23 x^4+2 e^{4 c_1}}}}{\sqrt {2}} \\ y(x)\to \frac {\sqrt {-5 x^2+\sqrt {23 x^4+2 e^{4 c_1}}}}{\sqrt {2}} \\ y(x)\to -\frac {\sqrt {-\sqrt {23} \sqrt {x^4}-5 x^2}}{\sqrt {2}} \\ y(x)\to \frac {\sqrt {-\sqrt {23} \sqrt {x^4}-5 x^2}}{\sqrt {2}} \\ y(x)\to -\frac {\sqrt {\sqrt {23} \sqrt {x^4}-5 x^2}}{\sqrt {2}} \\ y(x)\to \frac {\sqrt {\sqrt {23} \sqrt {x^4}-5 x^2}}{\sqrt {2}} \\ \end{align*}