Internal problem ID [11693]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 2, Miscellaneous Review. Exercises page 60
Problem number: 19.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {4 x y y^{\prime }-y^{2}=1} \] With initial conditions \begin {align*} [y \left (2\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 15
dsolve([4*x*y(x)*diff(y(x),x)=y(x)^2+1,y(2) = 1],y(x), singsol=all)
\[ y \left (x \right ) = \sqrt {\sqrt {2}\, \sqrt {x}-1} \]
✓ Solution by Mathematica
Time used: 3.741 (sec). Leaf size: 22
DSolve[{4*x*y[x]*y'[x]==y[x]^2+1,{y[2]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \sqrt {\sqrt {2} \sqrt {x}-1} \]