35.16 problem 1049

Internal problem ID [3762]

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]

Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{3}+\left (2 x -y^{2}\right ) \left (y^{\prime }\right )^{2}-2 x y^{2} y^{\prime }=0} \end {gather*}

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 \relax (x ) = \frac {1}{c_{1}-x} \\ y \relax (x ) = -x^{2}+c_{1} \\ y \relax (x ) = c_{1} \\ \end{align*}

Solution by Mathematica

Time used: 0.058 (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*}