Internal problem ID [3765]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 35
Problem number: 1052.
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}+x y^{2}+y^{4}\right ) \left (y^{\prime }\right )^{2}+x y^{2} \left (x^{2}+x y^{2}+y^{4}\right ) y^{\prime }-y^{6} x^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 89
dsolve(diff(y(x),x)^3-(x^2+x*y(x)^2+y(x)^4)*diff(y(x),x)^2+x*y(x)^2*(x^2+x*y(x)^2+y(x)^4)*diff(y(x),x)-x^3*y(x)^6 = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {x^{3}}{3}+c_{1} \\ y \relax (x ) = \frac {1}{\left (-3 x +c_{1}\right )^{\frac {1}{3}}} \\ y \relax (x ) = -\frac {1}{2 \left (-3 x +c_{1}\right )^{\frac {1}{3}}}-\frac {i \sqrt {3}}{2 \left (-3 x +c_{1}\right )^{\frac {1}{3}}} \\ y \relax (x ) = -\frac {1}{2 \left (-3 x +c_{1}\right )^{\frac {1}{3}}}+\frac {i \sqrt {3}}{2 \left (-3 x +c_{1}\right )^{\frac {1}{3}}} \\ y \relax (x ) = \frac {2}{-x^{2}+2 c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.226 (sec). Leaf size: 110
DSolve[(y'[x])^3 -(x^2+x y[x]^2+ y[x]^4) (y'[x])^2 +x y[x]^2(x^2 +x y[x]^2+ y[x]^4) y'[x]-x^3 y[x]^6==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt [3]{-\frac {1}{3}}}{\sqrt [3]{-x-c_1}} \\ y(x)\to \frac {1}{\sqrt [3]{3} \sqrt [3]{-x-c_1}} \\ y(x)\to \frac {(-1)^{2/3}}{\sqrt [3]{3} \sqrt [3]{-x-c_1}} \\ y(x)\to \frac {x^3}{3}+c_1 \\ y(x)\to -\frac {2}{x^2+2 c_1} \\ y(x)\to 0 \\ \end{align*}