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