64.6.19 problem 19

Internal problem ID [13369]
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
Date solved : Tuesday, January 28, 2025 at 05:33:04 AM
CAS classification : [_separable]

\begin{align*} 4 x y y^{\prime }&=1+y^{2} \end{align*}

With initial conditions

\begin{align*} y \left (2\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.107 (sec). Leaf size: 15

dsolve([4*x*y(x)*diff(y(x),x)=y(x)^2+1,y(2) = 1],y(x), singsol=all)
 

\[ y = \sqrt {\sqrt {x}\, \sqrt {2}-1} \]

✓ Solution by Mathematica

Time used: 3.545 (sec). Leaf size: 22

DSolve[{4*x*y[x]*D[y[x],x]==y[x]^2+1,{y[2]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \sqrt {\sqrt {2} \sqrt {x}-1} \]