Internal problem ID [4624]
Book: Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY.
2001
Section: Program 24. First order differential equations. Further problems 24. page 1068
Problem number: 46.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {x \left (1+y^{2}\right )-y \left (x^{2}+1\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 29
dsolve(x*(1+y(x)^2)-y(x)*(1+x^2)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \sqrt {c_{1} x^{2}+c_{1}-1} \\ y \relax (x ) = -\sqrt {c_{1} x^{2}+c_{1}-1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.421 (sec). Leaf size: 61
DSolve[x*(1+y[x]^2)-y[x]*(1+x^2)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {-1+e^{2 c_1} \left (x^2+1\right )} \\ y(x)\to \sqrt {-1+e^{2 c_1} \left (x^2+1\right )} \\ y(x)\to -i \\ y(x)\to i \\ \end{align*}