Internal problem ID [10225]
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.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {x^{2} \left (y^{\prime }\right )^{2}-\left (x -1\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve(x^2*diff(y(x),x)^2-(x-1)^2=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = x -\ln \relax (x )+c_{1} \\ y \relax (x ) = -x +\ln \relax (x )+c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 25
DSolve[x^2*(y'[x])^2-(x-1)^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x-\log (x)+c_1 \\ y(x)\to -x+\log (x)+c_1 \\ \end{align*}