Internal problem ID [2580]
Book: Differential equations and linear algebra, Stephen W. Goode, second edition,
2000
Section: 1.8, page 68
Problem number: 16.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _dAlembert]
\[ \boxed {y^{\prime }-\frac {y^{2}+2 y x -2 x^{2}}{x^{2}-y x +y^{2}}=0} \]
✓ Solution by Maple
Time used: 0.579 (sec). Leaf size: 79
dsolve(diff(y(x),x)= (y(x)^2+2*x*y(x)-2*x^2)/(x^2-x*y(x)+y(x)^2),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {x \left (\operatorname {RootOf}\left (2 \textit {\_Z}^{6}+\left (9 c_{1} x^{2}-1\right ) \textit {\_Z}^{4}-6 x^{2} c_{1} \textit {\_Z}^{2}+c_{1} x^{2}\right )^{2}-1\right )}{\operatorname {RootOf}\left (2 \textit {\_Z}^{6}+\left (9 c_{1} x^{2}-1\right ) \textit {\_Z}^{4}-6 x^{2} c_{1} \textit {\_Z}^{2}+c_{1} x^{2}\right )^{2}} \]
✓ Solution by Mathematica
Time used: 60.179 (sec). Leaf size: 373
DSolve[y'[x]== (y[x]^2+2*x*y[x]-2*x^2)/(x^2-x*y[x]+y[x]^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sqrt [3]{-54 x^3+2 \sqrt {729 x^6+\left (-9 x^2+3 e^{2 c_1}\right ){}^3}}}{3 \sqrt [3]{2}}-\frac {\sqrt [3]{2} \left (-3 x^2+e^{2 c_1}\right )}{\sqrt [3]{-54 x^3+2 \sqrt {729 x^6+\left (-9 x^2+3 e^{2 c_1}\right ){}^3}}}+x y(x)\to \frac {\left (-1+i \sqrt {3}\right ) \sqrt [3]{-54 x^3+2 \sqrt {729 x^6+\left (-9 x^2+3 e^{2 c_1}\right ){}^3}}}{6 \sqrt [3]{2}}+\frac {\left (1+i \sqrt {3}\right ) \left (-3 x^2+e^{2 c_1}\right )}{2^{2/3} \sqrt [3]{-54 x^3+2 \sqrt {729 x^6+\left (-9 x^2+3 e^{2 c_1}\right ){}^3}}}+x y(x)\to -\frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{-54 x^3+2 \sqrt {729 x^6+\left (-9 x^2+3 e^{2 c_1}\right ){}^3}}}{6 \sqrt [3]{2}}+\frac {\left (1-i \sqrt {3}\right ) \left (-3 x^2+e^{2 c_1}\right )}{2^{2/3} \sqrt [3]{-54 x^3+2 \sqrt {729 x^6+\left (-9 x^2+3 e^{2 c_1}\right ){}^3}}}+x \end{align*}