69.1.39 problem 58

Internal problem ID [14192]
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
Date solved : Tuesday, January 28, 2025 at 06:21:24 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }-\frac {a y}{x}&=\frac {1+x}{x} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 31

dsolve(diff(y(x),x)-a*y(x)/x=(x+1)/x,y(x), singsol=all)
 

\[ y = \left (-\frac {x^{-a} \left (a x +a -1\right )}{a \left (a -1\right )}+c_{1} \right ) x^{a} \]

✓ Solution by Mathematica

Time used: 1.116 (sec). Leaf size: 28

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

\[ y(x)\to -\frac {a x+a-1}{(a-1) a}+c_1 x^a \]