Internal problem ID [4553]
Book: Basic Training in Mathematics. By R. Shankar. Plenum Press. NY. 1995
Section: Chapter 10, Differential equations. Section 10.3, ODEs with variable Coefficients. First order.
page 315
Problem number: 10.3.8.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {\left (x^{2}+1\right ) y^{\prime }-x y-1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 15
dsolve((1+x^2)*diff(y(x),x)=1+x*y(x),y(x), singsol=all)
\[ y \relax (x ) = \sqrt {x^{2}+1}\, c_{1}+x \]
✓ Solution by Mathematica
Time used: 0.036 (sec). Leaf size: 19
DSolve[(1+x^2)*y'[x]==1+x*y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x+c_1 \sqrt {x^2+1} \\ \end{align*}