Internal problem ID [4270]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 35
Problem number: 1049.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [_quadrature]
\[ \boxed {{y^{\prime }}^{3}+\left (2 x -y^{2}\right ) {y^{\prime }}^{2}-2 x y^{2} y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 25
dsolve(diff(y(x),x)^3+(2*x-y(x)^2)*diff(y(x),x)^2-2*x*y(x)^2*diff(y(x),x) = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {1}{c_{1} -x} y \left (x \right ) = -x^{2}+c_{1} y \left (x \right ) = c_{1} \end{align*}
✓ Solution by Mathematica
Time used: 0.056 (sec). Leaf size: 31
DSolve[(y'[x])^3 +(2 x-y[x]^2) (y'[x])^2 -2 x y[x]^2 y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{x+c_1} y(x)\to c_1 y(x)\to -x^2+c_1 \end{align*}