Internal problem ID [1984]
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: 23.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]
\[ \boxed {\left (x^{2}+y^{2}-2 y\right ) y^{\prime }=2 x} \] With initial conditions \begin {align*} [y \left (1\right ) = 0] \end {align*}
✗ Solution by Maple
dsolve([(x^2+y(x)^2-2*y(x))*diff(y(x),x)=2*x,y(1) = 0],y(x), singsol=all)
\[ \text {No solution found} \]
✓ Solution by Mathematica
Time used: 0.159 (sec). Leaf size: 29
DSolve[{(x^2+y[x]^2-2*y[x])*y'[x]==2*x,{y[1]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [x^2 \left (-e^{-y(x)}\right )-e^{-y(x)} y(x)^2=-1,y(x)\right ] \]