82.13.1 problem Ex. 1

Internal problem ID [18801]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter III. Equations of the first order but not of the first degree. Problems at page 32
Problem number : Ex. 1
Date solved : Tuesday, January 28, 2025 at 12:18:34 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 25

dsolve(diff(y(x),x)^3+2*x*diff(y(x),x)^2-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: 0.040 (sec). Leaf size: 31

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