Internal problem ID [2057]
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: 26.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {-y^{\prime } y x=-3 x +6} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve(3*(x-2)=x*y(x)*diff(y(x),x),y(x), singsol=all)
\begin{align*} y = \sqrt {-12 \ln \left (x \right )+c_{1} +6 x} y = -\sqrt {-12 \ln \left (x \right )+c_{1} +6 x} \end{align*}
✓ Solution by Mathematica
Time used: 0.073 (sec). Leaf size: 50
DSolve[3*(x-2)==x*y[x]*y'[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {2} \sqrt {3 x-6 \log (x)+c_1} y(x)\to \sqrt {2} \sqrt {3 x-6 \log (x)+c_1} \end{align*}