Internal problem ID [2635]
Book: An introduction to the solution and applications of differential equations, J.W. Searl,
1966
Section: Chapter 4, Ex. 4.2
Problem number: 5.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {x \left (1+y^{2}\right )}{y \left (x^{2}+1\right )}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 13
dsolve([diff(y(x),x)=(x*(1+y(x)^2))/(y(x)*(1+x^2)),y(0) = 1],y(x), singsol=all)
\[ y \relax (x ) = \sqrt {2 x^{2}+1} \]
✓ Solution by Mathematica
Time used: 0.546 (sec). Leaf size: 16
DSolve[{y'[x]==(x*(1+y[x]^2))/(y[x]*(1+x^2)),y[0]==1},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt {2 x^2+1} \\ \end{align*}