64.6.21 problem 21

Internal problem ID [13371]
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
Date solved : Tuesday, January 28, 2025 at 05:33:16 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (\sqrt {15}\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 13

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

\[ y = \frac {\sqrt {x^{2}+1}}{2} \]

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 18

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

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