62.20.1 problem Ex 1

Internal problem ID [12915]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter V, Singular solutions. Article 33. Page 73
Problem number : Ex 1
Date solved : Tuesday, January 28, 2025 at 04:43:23 AM
CAS classification : [_quadrature]

\begin{align*} x^{2} {y^{\prime }}^{2}-\left (x -1\right )^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 21

dsolve(x^2*diff(y(x),x)^2-(x-1)^2=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 35

DSolve[x^2*(D[y[x],x])^2-(x-1)^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -x+\log (x)+c_1 \\ y(x)\to \int _1^x\left (1-\frac {1}{K[1]}\right )dK[1]+c_1 \\ \end{align*}