60.1.94 problem 94

Internal problem ID [10108]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 94
Date solved : Monday, January 27, 2025 at 06:27:47 PM
CAS classification : [_linear]

\begin{align*} x y^{\prime }+a y+b \,x^{n}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 23

dsolve(x*diff(y(x),x) +a*y(x) + b*x^n=0,y(x), singsol=all)
 

\[ y = -\frac {x^{n} b}{a +n}+x^{-a} c_{1} \]

✓ Solution by Mathematica

Time used: 0.071 (sec). Leaf size: 25

DSolve[x*D[y[x],x] +a*y[x] + b*x^n==0,y[x],x,IncludeSingularSolutions -> True]
 

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