Internal problem ID [3340]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 21
Problem number: 598.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {\left (x^{2}+y^{2}\right ) y^{\prime }+y x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.704 (sec). Leaf size: 223
dsolve((x^2+y(x)^2)*diff(y(x),x)+x*y(x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\sqrt {x^{2} c_{1} \left (c_{1} x^{2}+\sqrt {x^{4} c_{1}^{2}+1}\right )}}{x \left (c_{1} x^{2}+\sqrt {x^{4} c_{1}^{2}+1}\right ) c_{1}} \\ y \relax (x ) = \frac {\sqrt {-x^{2} c_{1} \left (-c_{1} x^{2}+\sqrt {x^{4} c_{1}^{2}+1}\right )}}{x \left (c_{1} x^{2}-\sqrt {x^{4} c_{1}^{2}+1}\right ) c_{1}} \\ y \relax (x ) = -\frac {\sqrt {x^{2} c_{1} \left (c_{1} x^{2}+\sqrt {x^{4} c_{1}^{2}+1}\right )}}{x \left (c_{1} x^{2}+\sqrt {x^{4} c_{1}^{2}+1}\right ) c_{1}} \\ y \relax (x ) = -\frac {\sqrt {-x^{2} c_{1} \left (-c_{1} x^{2}+\sqrt {x^{4} c_{1}^{2}+1}\right )}}{x \left (c_{1} x^{2}-\sqrt {x^{4} c_{1}^{2}+1}\right ) c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 8.67 (sec). Leaf size: 218
DSolve[(x^2+y[x]^2)y'[x]+x y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {-x^2-\sqrt {x^4+e^{4 c_1}}} \\ y(x)\to \sqrt {-x^2-\sqrt {x^4+e^{4 c_1}}} \\ y(x)\to -\sqrt {-x^2+\sqrt {x^4+e^{4 c_1}}} \\ y(x)\to \sqrt {-x^2+\sqrt {x^4+e^{4 c_1}}} \\ y(x)\to 0 \\ y(x)\to -\sqrt {-\sqrt {x^4}-x^2} \\ y(x)\to \sqrt {-\sqrt {x^4}-x^2} \\ y(x)\to -\sqrt {\sqrt {x^4}-x^2} \\ y(x)\to \sqrt {\sqrt {x^4}-x^2} \\ \end{align*}