Internal problem ID [12223]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 185.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {\left (x^{2}+1\right ) y^{\prime }-y x=\alpha } \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve((1+x^2)*diff(y(x),x)-x*y(x)-alpha=0,y(x), singsol=all)
\[ y \left (x \right ) = \alpha x +c_{1} \sqrt {x^{2}+1} \]
✓ Solution by Mathematica
Time used: 0.114 (sec). Leaf size: 21
DSolve[(1+x^2)*y'[x]-x*y[x]-a==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to a x+c_1 \sqrt {x^2+1} \]