62.19.1 problem Ex 5

Internal problem ID [12914]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter V, Singular solutions. Article 32. Page 69
Problem number : Ex 5
Date solved : Tuesday, January 28, 2025 at 04:43:22 AM
CAS classification : [[_homogeneous, `class G`], _Clairaut]

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

✓ Solution by Maple

Time used: 0.096 (sec). Leaf size: 35

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

\begin{align*} y &= \frac {1}{x} \\ y &= c_{1} x -2 \sqrt {-c_{1}} \\ y &= c_{1} x +2 \sqrt {-c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.334 (sec). Leaf size: 49

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

\begin{align*} y(x)\to \frac {4 (x+i c_1)}{c_1{}^2} \\ y(x)\to \frac {4 (x-i c_1)}{c_1{}^2} \\ y(x)\to 0 \\ y(x)\to \frac {1}{x} \\ \end{align*}