Internal problem ID [8872]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 537.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries]]
\[ \boxed {x^{3} {y^{\prime }}^{3}-3 x^{2} y {y^{\prime }}^{2}+\left (3 x y^{2}+x^{6}\right ) y^{\prime }-y^{3}-2 y x^{5}=0} \]
✗ Solution by Maple
dsolve(x^3*diff(y(x),x)^3-3*x^2*y(x)*diff(y(x),x)^2+(3*x*y(x)^2+x^6)*diff(y(x),x)-y(x)^3-2*x^5*y(x)=0,y(x), singsol=all)
\[ \text {No solution found} \]
✓ Solution by Mathematica
Time used: 0.059 (sec). Leaf size: 15
DSolve[-2*x^5*y[x] - y[x]^3 + (x^6 + 3*x*y[x]^2)*y'[x] - 3*x^2*y[x]*y'[x]^2 + x^3*y'[x]^3==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 x \left (x+c_1{}^2\right ) \]