82.23.3 problem Ex. 3

Internal problem ID [18859]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter IV. Singular solutions. problems on chapter IV. page 49
Problem number : Ex. 3
Date solved : Tuesday, January 28, 2025 at 12:31:06 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, _Clairaut]

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

✓ Solution by Maple

Time used: 0.049 (sec). Leaf size: 64

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

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

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

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

Timed out