Internal problem ID [4611]
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: 33.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left (x^{2}+1\right ) y^{\prime }-x \left (y+1\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve((1+x^2)*diff(y(x),x)=x*(1+y(x)),y(x), singsol=all)
\[ y \relax (x ) = \sqrt {x^{2}+1}\, c_{1}-1 \]
✓ Solution by Mathematica
Time used: 0.054 (sec). Leaf size: 24
DSolve[(1+x^2)*y'[x]==x*(1+y[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -1+c_1 \sqrt {x^2+1} \\ y(x)\to -1 \\ \end{align*}