69.1.126 problem 185

Internal problem ID [14279]
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
Date solved : Tuesday, January 28, 2025 at 06:25:26 AM
CAS classification : [_linear]

\begin{align*} \left (x^{2}+1\right ) y^{\prime }-y x -\alpha &=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

dsolve((1+x^2)*diff(y(x),x)-x*y(x)-alpha=0,y(x), singsol=all)
 

\[ y = c_{1} \sqrt {x^{2}+1}+\alpha x \]

✓ Solution by Mathematica

Time used: 0.051 (sec). Leaf size: 21

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

\[ y(x)\to a x+c_1 \sqrt {x^2+1} \]