Internal problem ID [2086]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 12, page 46
Problem number: 57.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {2 \left (x^{2}+1\right ) y^{\prime }-\left (2 y^{2}-1\right ) x y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 17
dsolve([2*(1+x^2)*diff(y(x),x)=(2*y(x)^2-1)*x*y(x),y(0) = 1],y(x), singsol=all)
\[ y = \frac {1}{\sqrt {2-\sqrt {x^{2}+1}}} \]
✓ Solution by Mathematica
Time used: 4.797 (sec). Leaf size: 32
DSolve[{2*(1+x^2)*y'[x]==(2*y[x]^2-1)*x*y[x],{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {\sqrt {-\sqrt {x^2+1}-2}}{\sqrt {x^2-3}} \]