Internal problem ID [2336]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 37, page 171
Problem number: 23.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational]
\[ \boxed {-3 y^{\prime } y+{y^{\prime }}^{2} x=-x^{2}} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 43
dsolve(x^2-3*diff(y(x),x)*y(x)+x*diff(y(x),x)^2=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {4 x^{3}+c_{1}^{2}}{6 c_{1}} y \left (x \right ) = \frac {c_{1}^{2} x^{3}+4}{6 c_{1}} y \left (x \right ) = c_{1} x^{\frac {3}{2}} \end{align*}
✓ Solution by Mathematica
Time used: 0.293 (sec). Leaf size: 83
DSolve[x^2-3*y'[x]*y[x]+x*y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{6} e^{-\frac {3 c_1}{2}} \left (4 x^3+e^{3 c_1}\right ) y(x)\to \frac {1}{6} e^{-\frac {3 c_1}{2}} \left (4 x^3+e^{3 c_1}\right ) y(x)\to -\frac {2 x^{3/2}}{3} y(x)\to \frac {2 x^{3/2}}{3} \end{align*}