Internal problem ID [8106]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 526.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{3}-\left (y^{2}+y x +x^{2}\right ) \left (y^{\prime }\right )^{2}+\left (x y^{3}+y^{2} x^{2}+y x^{3}\right ) y^{\prime }-y^{3} x^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 32
dsolve(diff(y(x),x)^3-(y(x)^2+x*y(x)+x^2)*diff(y(x),x)^2+(x*y(x)^3+x^2*y(x)^2+x^3*y(x))*diff(y(x),x)-x^3*y(x)^3=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {x^{3}}{3}+c_{1} \\ y \relax (x ) = \frac {1}{c_{1}-x} \\ y \relax (x ) = {\mathrm e}^{\frac {x^{2}}{2}} c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.12 (sec). Leaf size: 48
DSolve[-(x^3*y[x]^3) + (x^3*y[x] + x^2*y[x]^2 + x*y[x]^3)*y'[x] - (x^2 + x*y[x] + y[x]^2)*y'[x]^2 + y'[x]^3==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{x+c_1} \\ y(x)\to c_1 e^{\frac {x^2}{2}} \\ y(x)\to \frac {x^3}{3}+c_1 \\ y(x)\to 0 \\ \end{align*}