82.18.22 problem Ex. 24

Internal problem ID [18844]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter III. Equations of the first order but not of the first degree. Examples on chapter III. page 38
Problem number : Ex. 24
Date solved : Tuesday, January 28, 2025 at 12:26:46 PM
CAS classification : [`y=_G(x,y')`]

\begin{align*} \left (1-y^{2}+\frac {y^{4}}{x^{2}}\right ) {y^{\prime }}^{2}-\frac {2 y y^{\prime }}{x}+\frac {y^{2}}{x^{2}}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.161 (sec). Leaf size: 59

dsolve((1-y(x)^2+y(x)^4/x^2)*diff(y(x),x)^2-2*y(x)/x*diff(y(x),x)+y(x)^2/x^2=0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= -x \\ y \left (x \right ) &= x \\ y \left (x \right ) &= 0 \\ y \left (x \right ) &= -\operatorname {arctanh}\left (\operatorname {RootOf}\left (\operatorname {arctanh}\left (\textit {\_Z} \right )^{2} \textit {\_Z}^{2}-2 \,\operatorname {arctanh}\left (\textit {\_Z} \right ) c_{1} \textit {\_Z}^{2}+c_{1}^{2} \textit {\_Z}^{2}-x^{2} \textit {\_Z}^{2}+x^{2}\right )\right )+c_{1} \\ \end{align*}

✗ Solution by Mathematica

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

DSolve[(1-y[x]^2+y[x]^4/x^2)*D[y[x],x]^2-2*y[x]/x*D[y[x],x]+y[x]^2/x^2==0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved