Internal problem ID [6151]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\frac {y^{\prime }}{x^{2}+1}-\frac {x}{y}=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 20
dsolve([diff(y(x),x)/(1+x^2)=x/y(x),y(1) = 3],y(x), singsol=all)
\[ y \left (x \right ) = \frac {\sqrt {2 x^{4}+4 x^{2}+30}}{2} \]
✓ Solution by Mathematica
Time used: 0.104 (sec). Leaf size: 25
DSolve[{y'[x]/(1+x^2)==x/y[x],{y[1]==3}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {\sqrt {x^4+2 x^2+15}}{\sqrt {2}} \]