Internal problem ID [5296]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 5. Equations of first order and first degree (Exact equations). Supplemetary
problems. Page 33
Problem number: 26 (i).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _dAlembert]
\[ \boxed {y \left (y^{2}-2 x^{2}\right )+x \left (2 y^{2}-x^{2}\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.109 (sec). Leaf size: 69
dsolve(y(x)*(y(x)^2-2*x^2)+x*(2*y(x)^2-x^2)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y = \sqrt {\frac {\frac {c_{1} x^{3}}{2}-\frac {\sqrt {c_{1}^{2} x^{6}+4}}{2}}{c_{1} x^{3}}}\, x y = \sqrt {\frac {\frac {c_{1} x^{3}}{2}+\frac {\sqrt {c_{1}^{2} x^{6}+4}}{2}}{c_{1} x^{3}}}\, x \end{align*}
✓ Solution by Mathematica
Time used: 11.861 (sec). Leaf size: 277
DSolve[y[x]*(y[x]^2-2*x^2)+x*(2*y[x]^2-x^2)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {x^2-\frac {\sqrt {x^6-4 e^{2 c_1}}}{x}}}{\sqrt {2}} y(x)\to \frac {\sqrt {x^2-\frac {\sqrt {x^6-4 e^{2 c_1}}}{x}}}{\sqrt {2}} y(x)\to -\frac {\sqrt {\frac {x^3+\sqrt {x^6-4 e^{2 c_1}}}{x}}}{\sqrt {2}} y(x)\to \frac {\sqrt {\frac {x^3+\sqrt {x^6-4 e^{2 c_1}}}{x}}}{\sqrt {2}} y(x)\to -\frac {\sqrt {x^2-\frac {\sqrt {x^6}}{x}}}{\sqrt {2}} y(x)\to \frac {\sqrt {x^2-\frac {\sqrt {x^6}}{x}}}{\sqrt {2}} y(x)\to -\frac {\sqrt {\frac {\sqrt {x^6}+x^3}{x}}}{\sqrt {2}} y(x)\to \frac {\sqrt {\frac {\sqrt {x^6}+x^3}{x}}}{\sqrt {2}} \end{align*}