62.17.9 problem Ex 9

Internal problem ID [12909]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter IV, differential equations of the first order and higher degree than the first. Article 28. Summary. Page 59
Problem number : Ex 9
Date solved : Tuesday, January 28, 2025 at 04:43:02 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 0.048 (sec). Leaf size: 26

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

\begin{align*} y(x)\to c_1 (x-2) \\ y(x)\to c_1 (x+2) \\ y(x)\to 0 \\ \end{align*}