29.21.22 problem 598

Internal problem ID [5192]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 21
Problem number : 598
Date solved : Monday, January 27, 2025 at 10:18:40 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 1.182 (sec). Leaf size: 221

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

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

✓ Solution by Mathematica

Time used: 9.277 (sec). Leaf size: 218

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