Internal problem ID [12456]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 58.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }-\frac {a y}{x}=\frac {x +1}{x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve(diff(y(x),x)-a*y(x)/x=(x+1)/x,y(x), singsol=all)
\[ y \left (x \right ) = \left (-\frac {x^{-a} \left (a x +a -1\right )}{a \left (a -1\right )}+c_{1} \right ) x^{a} \]
✓ Solution by Mathematica
Time used: 0.136 (sec). Leaf size: 28
DSolve[y'[x]-a*y[x]/x==(x+1)/x,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {a x+a-1}{(a-1) a}+c_1 x^a \]