29.35.16 problem 1049

Internal problem ID [5614]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 35
Problem number : 1049
Date solved : Monday, January 27, 2025 at 12:26:49 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.005 (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}{-x +c_{1}} \\ y \left (x \right ) &= -x^{2}+c_{1} \\ y \left (x \right ) &= c_{1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.062 (sec). Leaf size: 31

DSolve[(D[y[x],x])^3 +(2*x-y[x]^2)*(D[y[x],x])^2 -2*x*y[x]^2 D[y[x],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*}