Internal problem ID [1985]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 9, page 38
Problem number: 24.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]
\[ \boxed {y-x^{2} \sqrt {x^{2}-y^{2}}-y^{\prime } x=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 1] \end {align*}
✗ Solution by Maple
dsolve([(y(x)-x^2*sqrt(x^2-y(x)^2))-x*diff(y(x),x)=0,y(1) = 1],y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[{(y[x]-x^2*Sqrt[x^2-y[x]^2])-x*y'[x]==0,{y[1]==1}},y[x],x,IncludeSingularSolutions -> True]
{}