Internal problem ID [4280]
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]
\[ \boxed {x {y^{\prime }}^{3}-\left (x +x^{2}+y\right ) {y^{\prime }}^{2}+\left (x^{2}+y+y x \right ) y^{\prime }-y x=0} \]
✓ Solution by Maple
Time used: 0.0 (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 \left (x \right ) = c_{1} x y \left (x \right ) = x +c_{1} y \left (x \right ) = \frac {x^{2}}{2}+c_{1} \end{align*}
✓ Solution by Mathematica
Time used: 0.044 (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*}