6.21 problem 21

Internal problem ID [11695]

Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section: Chapter 2, Miscellaneous Review. Exercises page 60
Problem number: 21.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_separable]

\[ \boxed {y^{\prime }-\frac {x y}{x^{2}+1}=0} \] With initial conditions \begin {align*} \left [y \left (\sqrt {15}\right ) = 2\right ] \end {align*}

Solution by Maple

Time used: 0.015 (sec). Leaf size: 13

dsolve([diff(y(x),x)=(x*y(x))/(x^2+1),y(15^(1/2)) = 2],y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\sqrt {x^{2}+1}}{2} \]

Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 18

DSolve[{y'[x]==(x*y[x])/(x^2+1),{y[Sqrt[15]]==2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\sqrt {x^2+1}}{2} \]