82.16.1 problem Ex. 1

Internal problem ID [18815]
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 36
Problem number : Ex. 1
Date solved : Tuesday, January 28, 2025 at 12:21:21 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.024 (sec). Leaf size: 33

dsolve(y(x)^2+x*y(x)*diff(y(x),x)-x^2*diff(y(x),x)^2=0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= 0 \\ y \left (x \right ) &= c_{1} x^{\frac {1}{2}-\frac {\sqrt {5}}{2}} \\ y \left (x \right ) &= c_{1} x^{\frac {1}{2}+\frac {\sqrt {5}}{2}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.075 (sec). Leaf size: 48

DSolve[y[x]^2+x*y[x]*D[y[x],x]-x^2*D[y[x],x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 x^{\frac {1}{2}-\frac {\sqrt {5}}{2}} \\ y(x)\to c_1 x^{\frac {1}{2} \left (1+\sqrt {5}\right )} \\ y(x)\to 0 \\ \end{align*}