Internal problem ID [1956]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 8, page 34
Problem number: 15.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _exact, _rational, [_Abel, `2nd type`, `class B`]]
\[ \boxed {\frac {y \left (2+y x^{3}\right )}{x^{3}}-\frac {\left (1-2 y x^{3}\right ) y^{\prime }}{x^{2}}=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 57
dsolve(y(x)*(2+x^3*y(x))/x^3=(1-2*x^3*y(x))/x^2*diff(y(x),x),y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {c_{1}^{3}-\sqrt {c_{1}^{6}+4 c_{1} x^{5}}}{2 x^{3} c_{1}^{3}} \\ y \left (x \right ) &= \frac {c_{1}^{3}+\sqrt {c_{1}^{6}+4 c_{1} x^{5}}}{2 c_{1}^{3} x^{3}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.861 (sec). Leaf size: 80
DSolve[y[x]*(2+x^3*y[x])/x^3==(1-2*x^3*y[x])/x^2*y'[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1-\sqrt {\frac {1}{x^3}} x^2 \sqrt {\frac {1}{x}+4 c_1 x^4}}{2 x^3} \\ y(x)\to \frac {1+\sqrt {\frac {1}{x^3}} x^2 \sqrt {\frac {1}{x}+4 c_1 x^4}}{2 x^3} \\ \end{align*}