50.2.13 problem 2(c)

Internal problem ID [7819]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.3 SEPARABLE EQUATIONS. Page 12
Problem number : 2(c)
Date solved : Monday, January 27, 2025 at 03:24:06 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (1\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 0.047 (sec). Leaf size: 20

dsolve([diff(y(x),x)/(1+x^2)=x/y(x),y(1) = 3],y(x), singsol=all)
 

\[ y = \frac {\sqrt {2 x^{4}+4 x^{2}+30}}{2} \]

✓ Solution by Mathematica

Time used: 0.109 (sec). Leaf size: 25

DSolve[{D[y[x],x]/(1+x^2)==x/y[x],{y[1]==3}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\sqrt {x^4+2 x^2+15}}{\sqrt {2}} \]