27.2.5 problem 5

Internal problem ID [4305]
Book : An introduction to the solution and applications of differential equations, J.W. Searl, 1966
Section : Chapter 4, Ex. 4.2
Problem number : 5
Date solved : Monday, January 27, 2025 at 09:00:50 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.028 (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)
 

\[ y \left (x \right ) = \sqrt {2 x^{2}+1} \]

✓ Solution by Mathematica

Time used: 0.523 (sec). Leaf size: 16

DSolve[{D[y[x],x]==(x*(1+y[x]^2))/(y[x]*(1+x^2)),y[0]==1},y[x],x,IncludeSingularSolutions -> True]
 

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