Internal problem ID [3772]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 35
Problem number: 1060.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {x \left (y^{\prime }\right )^{3}-\left (x +x^{2}+y\right ) \left (y^{\prime }\right )^{2}+\left (x^{2}+y+y x \right ) y^{\prime }-y x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 23
dsolve(x*diff(y(x),x)^3-(x+x^2+y(x))*diff(y(x),x)^2+(x^2+y(x)+x*y(x))*diff(y(x),x)-x*y(x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = c_{1} x \\ y \relax (x ) = c_{1}+x \\ y \relax (x ) = \frac {x^{2}}{2}+c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.042 (sec). Leaf size: 36
DSolve[x (y'[x])^3 - (x+x^2+y[x])(y'[x])^2 + (x^2+y[x]+x y[x]) y'[x]-x y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 x \\ y(x)\to x+c_1 \\ y(x)\to \frac {x^2}{2}+c_1 \\ y(x)\to 0 \\ \end{align*}