83.23.27 problem 27

Internal problem ID [19308]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter V. Singular solutions. Exercise V at page 76
Problem number : 27
Date solved : Tuesday, January 28, 2025 at 01:30:34 PM
CAS classification : [`y=_G(x,y')`]

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

✗ Solution by Maple

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

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

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

Not solved