Internal problem ID [15068]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 7, Total differential equations. The integrating factor. Exercises page
61
Problem number: 179.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class D`], _exact, _rational]
\[ \boxed {\frac {x^{2}+y^{2}}{x^{2} y}-\frac {\left (x^{2}+y^{2}\right ) y^{\prime }}{y^{2} x}=-2 x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 65
dsolve((2*x+ (x^2+y(x)^2)/(x^2*y(x)) )=( (x^2+y(x)^2)/(x*y(x)^2) )*diff(y(x),x),y(x), singsol=all)
\begin{align*} y \left (x \right ) &= -\frac {\left (-x^{2}+\sqrt {x^{4}+4 c_{1} x^{2}+4 c_{1}^{2}+4}-2 c_{1} \right ) x}{2} \\ y \left (x \right ) &= \frac {\left (x^{2}+2 c_{1} +\sqrt {x^{4}+4 c_{1} x^{2}+4 c_{1}^{2}+4}\right ) x}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.364 (sec). Leaf size: 78
DSolve[(2*x+ (x^2+y[x]^2)/(x^2*y[x]) )==( (x^2+y[x]^2)/(x*y[x]^2) )*y'[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} x \left (x^2-\sqrt {x^4+2 c_1 x^2+4+c_1{}^2}+c_1\right ) \\ y(x)\to \frac {1}{2} x \left (x^2+\sqrt {x^4+2 c_1 x^2+4+c_1{}^2}+c_1\right ) \\ y(x)\to 0 \\ \end{align*}