Internal problem ID [3764]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 35
Problem number: 1051.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{3}-\left (x^{2}+y x +y^{2}\right ) \left (y^{\prime }\right )^{2}+x y \left (x^{2}+y x +y^{2}\right ) y^{\prime }-y^{3} x^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 32
dsolve(diff(y(x),x)^3-(x^2+x*y(x)+y(x)^2)*diff(y(x),x)^2+x*y(x)*(x^2+x*y(x)+y(x)^2)*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 ) = c_{1} {\mathrm e}^{\frac {x^{2}}{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.097 (sec). Leaf size: 48
DSolve[(y'[x])^3 -(x^2+x y[x]+ y[x]^2) (y'[x])^2 +x y[x](x^2 +x y[x]+ y[x]^2) y'[x]-x^3 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*}