Internal problem ID [2059]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 12, page 46
Problem number: 28.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, _Bernoulli]
\[ \boxed {2 y^{\prime } x -y+\frac {x^{2}}{y^{2}}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 93
dsolve(2*x*diff(y(x),x)-y(x)+x^2/y(x)^2=0,y(x), singsol=all)
\begin{align*} y = \left (x^{\frac {3}{2}} c_{1} -3 x^{2}\right )^{\frac {1}{3}} y = -\frac {\left (x^{\frac {3}{2}} c_{1} -3 x^{2}\right )^{\frac {1}{3}}}{2}-\frac {i \sqrt {3}\, \left (x^{\frac {3}{2}} c_{1} -3 x^{2}\right )^{\frac {1}{3}}}{2} y = -\frac {\left (x^{\frac {3}{2}} c_{1} -3 x^{2}\right )^{\frac {1}{3}}}{2}+\frac {i \sqrt {3}\, \left (x^{\frac {3}{2}} c_{1} -3 x^{2}\right )^{\frac {1}{3}}}{2} \end{align*}
✓ Solution by Mathematica
Time used: 3.57 (sec). Leaf size: 80
DSolve[2*x*y'[x]-y[x]+x^2/y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt [3]{-3 x^2+c_1 x^{3/2}} y(x)\to -\sqrt [3]{-1} \sqrt [3]{-3 x^2+c_1 x^{3/2}} y(x)\to (-1)^{2/3} \sqrt [3]{-3 x^2+c_1 x^{3/2}} \end{align*}