Internal problem ID [8875]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 540.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [_quadrature]
\[ \boxed {2 y {y^{\prime }}^{3}-y {y^{\prime }}^{2}+2 y^{\prime } x=x} \]
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 109
dsolve(2*y(x)*diff(y(x),x)^3-y(x)*diff(y(x),x)^2+2*x*diff(y(x),x)-x=0,y(x), singsol=all)
\begin{align*} x +\frac {x c_{1}}{\left (\frac {-\sqrt {-x y \left (x \right )}+y \left (x \right )}{y \left (x \right )}\right )^{\frac {2}{3}} y \left (x \right ) \left (\frac {-x +\sqrt {-x y \left (x \right )}+y \left (x \right )}{y \left (x \right )}\right )^{\frac {2}{3}}} = 0 x +\frac {x c_{1}}{\left (\frac {\sqrt {-x y \left (x \right )}+y \left (x \right )}{y \left (x \right )}\right )^{\frac {2}{3}} y \left (x \right ) \left (\frac {-x -\sqrt {-x y \left (x \right )}+y \left (x \right )}{y \left (x \right )}\right )^{\frac {2}{3}}} = 0 y \left (x \right ) = \frac {x}{2}+c_{1} \end{align*}
✓ Solution by Mathematica
Time used: 3.408 (sec). Leaf size: 61
DSolve[-x + 2*x*y'[x] - y[x]*y'[x]^2 + 2*y[x]*y'[x]^3==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x}{2}+c_1 y(x)\to \left (\frac {3 c_1}{2}-i x^{3/2}\right ){}^{2/3} y(x)\to \left (i x^{3/2}+\frac {3 c_1}{2}\right ){}^{2/3} \end{align*}