Internal problem ID [1946]
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: 4.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type
[_exact, _rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class A`]]
\[ \boxed {x \left (6 y x +5\right )+\left (2 x^{3}+3 y\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 55
dsolve(x*(6*x*y(x)+5)+(2*x^3+3*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y = -\frac {2 x^{3}}{3}-\frac {\sqrt {4 x^{6}-15 x^{2}-6 c_{1}}}{3} y = -\frac {2 x^{3}}{3}+\frac {\sqrt {4 x^{6}-15 x^{2}-6 c_{1}}}{3} \end{align*}
✓ Solution by Mathematica
Time used: 0.145 (sec). Leaf size: 69
DSolve[x*(6*x*y[x]+5)+(2*x^3+3*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{3} \left (-2 x^3-\sqrt {4 x^6-15 x^2+9 c_1}\right ) y(x)\to \frac {1}{3} \left (-2 x^3+\sqrt {4 x^6-15 x^2+9 c_1}\right ) \end{align*}